There are various anecdotes in the sources regarding Alexander as a boy.
Plutarch
In Plutarch, he questions the Persian ambassadors in Philip’s absence. It is unknown how old he was here, but he may have been ten or eleven as about this time the Persian Artabazus (Barsine’s father) returned to Persia having been an exile in Pella for several years, and it may have been as the result of an envoy from the Persian king.
Aeschines, Against TimarchusHe once entertained the envoys from the Persian king who came during Philip's absence, and associated with them freely. He won upon them by his friendliness, and by asking no childish or trivial questions, 2 but by enquiring about the length of the roads and the character of the journey into the interior, about the king himself, what sort of a warrior he was, and what the prowess and might of the Persians. 3 The envoys were therefore astonished and regarded the much-talked of ability of Philip as nothing compared with his son's eager disposition to do great things.
http://www.perseus.tufts.edu/hopper/tex ... te-link72
Aeschines and Demosthenes were amongst the Athenian delegates to Philip in 346 BC to ratify the peace treaty after Philip had repulsed the Athenians and Spartans at Thermoplyae. Timarchus and Demosthenes brought a suit against Aeschines “accusing him of misconduct as an ambassador”. Aeschines’ response sets out the Athenian laws, such as no man other than the teacher and his relatives being allowed inside a school, to protect free-born boys from the depredations of men. Alexander would have been ten at the time and was part of the entertainment for his father’s guests.
Pythian Games“But nevertheless, although all this is so plainly defined, many irrelevant arguments will be invented by Demosthenes. Possibly, when he sticks to his subject, we might be less indignant with him for the animosity he shows; but when, to the injury of our national rights, he foists in matters that do not belong to the case, then one may well be angry. Philip will be largely in evidence, and the name of Philip's son Alexander is going to be mixed up in it. For in addition to all the rest that is bad in him, this Demosthenes is an ill-mannered and boorish sort of person.
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His offensive talk against Philip is foolish and out of place, but not so serious a mistake as that which I am about to mention. For confessedly he will be making his slanderous charges against a man—he who is himself no man. But when he insinuates shameful suspicions against the boy, by deliberately applying to him words of double meaning, he makes our city ridiculous.
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For, under the impression that he is hurting me with reference to the accounting which I am about to render for my service on the embassy,71 he says that when the other day he himself was describing the boy Alexander, telling how at a certain banquet of ours he played the cithara, reciting certain passages in which there were thrusts at another boy, and when he reported to the senate what he himself happened to know about the incident, I got angry at his jests at the expense of the boy,72 as though I were not merely a member of the embassy, but one of the boy's own family.
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Now I naturally have had no conversation with Alexander, because of his youth, but Philip I do praise now because of his auspicious words, and if in what he does toward us in the future he shall fulfil the promise of what he now says, he will make praise of him a safe and easy thing. I did, indeed, rebuke Demosthenes in the senate-chamber, not because I was counting the favor of the boy, but because I felt that if you should listen to such words as his, the city would show itself as ill-behaved as the speaker.
72 The words of double meaning that Aeschines says Demosthenes applied to the boy Alexander would be connected with the story of this “playing” and “reciting.””
In August of that same year (346 BC), after the end of the Third Sacred War, Philip presided over the Pythian Games at Delphi. He may well have taken Alexander with him, although this is not mentioned in the sources.
Olympic Games
What is preserved in the Alexander Romances though is that Alexander, aged fifteen, visited the Olympic Games. Although the events as described are probably fictitious, they may preserve a grain of truth.
http://www.attalus.org/translate/alexander1b.html
In the Syriac version, Bucephalus, the man-eating horse, kills Nicolaus.“Alexander went to the harbour and gave orders that a new boat should be launched and the horses with their chariots embarked. Then he went on and with him his friend Hephaestion and they sailed to Pisa. Landing there and taking lodgings, he gave orders to his servants about the care of the horses, and then with Hephaestion started on a walk.
They were met by a man named Nicolaus, a fine young fellow, a prince of the Acarnanians, proud because he was relying on wealth and fortune, two undependable gods, and confident of his body's power. He came up and greeted Alexander and, wishing to learn why he was there, said: "Greetings, young gentleman." He replied: "And greetings also to you whoever you may be." The other said: "Whom, pray, do you think you are addressing? Nicolaus, king of the Acarnanians." And Alexander said: "Do not be so haughty, King Nicolaus, as though you had a sure hold on your life today. Fortune does not stand fixed on one spot, but her blow falls and beheads the proud." The other said: "You speak rightly. Now why have you come here? For I have learned that you are the son of Philip of Macedon. He said: "I am here to take part in the contests, not in the riding (for I am still too young) nor in the driving of two-horses or any other such sport." Nicolaus asked: "What then do you wish?" He said: "I wish to drive a chariot." Then Nicolaus, raging and despising Alexander's youth, for he had not learned the greatness of the spirit, spat at him and said: "A curse on you!" Alexander, who had learned self-control, wiping off the spittle, and smiling ominously, said: "Nicolaus, I swear by the holy sperm of my father and the holy womb of my mother, that even here I will conquer you in the chariot-race and in the country of the Acarnanians I will conquer you with my spear." After this conversation, they parted in wrath…..
The trumpet sounded the call to the contest. The starting-place was opened. All leaped forth on their cars. Then appeared the first contestant, the second, the third and the fourth. . . As for those coming in later, their horses were not well guided and had lost their spirit. The fourth driver was Alexander and behind him was Nicolaus, who did not wish the victory as much as the destruction of Alexander. For the father of Nicolaus had been killed by Philip in the war.
Alexander knew this and wisely contrived when the first horses fell, to let Nicolaus pass him. And Nicolaus, thinking that he had conquered Alexander, went on, hoping to be crowned as victor. But after two or three stades, the right horse of Nicolaus collapsed and the whole chariot with the charioteer himself was overturned. And Alexander rushing on with his horses at full speed immediately killed Nicolaus. Alexander continued on. “
Bucephalus
Plutarch
Plutarch narrates the famous episode of Alexander taming Bucephalus. He is generally supposed to have been about thirteen here.
Once upon a time Philoneicus the Thessalian brought Bucephalas, offering to sell him to Philip for thirteen talents,7 and they went down into the plain to try the horse, who appeared to be savage and altogether intractable, neither allowing any one to mount him, nor heeding the voice of any of Philip's attendants, but rearing up against all of them. 2 Then Philip was vexed and ordered the horse to be led away, believing him to be altogether wild and unbroken; but Alexander, who was near by, said: "What a horse they are losing, because, for lack of skill and courage, they cannot manage him!" 3 At first, then, Philip held his peace; but as Alexander many times let fall such words and showed great distress, he said: "Dost thou find fault with thine elders in the belief that thou knowest more than they do or art better able to manage a horse?" p239 4 "This horse, at any rate," said Alexander, "I could manage better than others have." "And if thou shouldst not, what penalty wilt thou undergo for thy rashness?" "Indeed," said Alexander, "I will forfeit the price of the horse." 5 There was laughter at this, and then an agreement between father and son as to the forfeiture, and at once Alexander ran to the horse, took hold of his bridle-rein, and turned him towards the sun; for he had noticed, as it would seem, that the horse was greatly disturbed by the sight of his own shadow falling in front of him and dancing about. 6 And after he had calmed the horse a little in this way, and had stroked him with his hand, when he saw that he was full of spirit and courage, he quietly cast aside his mantle and with a light spring safely bestrode him. 7 Then, with a little pressure of the reins on the bit, and without striking him or tearing his mouth, he held him in hand;8 but when he saw that the horse was rid of the fear that had beset him, and was impatient for the course, he gave him his head, and at last urged him on with sterner tone and thrust of foot. 8 Philip and his company were speechless with anxiety at first; but when Alexander made the turn in proper fashion and came back to them proud and exultant, all the rest broke into loud cries, but his father, as we are told, actually shed tears of joy, and when Alexander had dismounted, kissed him, saying: "My son, seek thee out a kingdom equal to thyself; Macedonia has not room for thee."