According to Josephus, Ant. 17, 1, 3 in about 9 BCE Archelaus, Herod Antipas and Philip
were sent to Rome for further education. There they stayed privately with a family, maybe with Asinius Pollio.
I imagine that Jesus, being in the entourage of the princes, also went to Rome and got the same education. Herod the Great and his successors needed competent experts for the administration and Rome-educated diplomats who were loyal to the Herod family.
For the Romans it was important to educate members of the elites of the subject nations, who could transmit Roman principles of government to their homelands.
They studied the artes liberales, subjects for free-born young men, which did not require hard manual work: grammar, rhetoric, dialectics, arithmetic, geometry, astronomy (which included astrology), music theory.
In Rome, the Jewish students had to learn Latin, the language of the rulers of the world.