Answer:
He would be living in a royal palace, where among the other things he would be preparing himself for the role that awaits him, and that is to inherit his father's throne.
Step-by-step explanation:
Of course, we need to have in mind that different city states in Greece had different systems. But, for example in some them we had established dynasties. Therefore, it was quite often that a ruler's son is living in the palace of this father. As a heir of throne he was highly respected on it.