In terms of tactics? Most likely the Phalanxes of Alexander the Great's armies, or even the hoplites of the Spartans. The Spartans are probably more of an influence because they were trained for war from birth, and surpassed most groups in their close-order combat style. Of course they could be beaten but I think they are definitely an influence.

Another possibility are the Mamelukes. Used throughout the Middle East (and for a long period of time), Mamelukes were bought as slaves from Turkic tribes and trained into professional troops over time. This is similar in some ways to the Janissaries that /u/SchurkjeBoefje mentioned, and like the Janissaries they eventually obtained a high level of political power, even setting up a dynasty that controlled Egypt for a prolonged period of time.

Source: Hathaway, Jane (February 1995). "The Military Household in Ottoman Egypt". International Journal of Middle East Studies

A whole lot of them, I'm sure. The only influence I can clearly distinguish myself is the slave-soldier parallel with Ottoman Janissaries. They started as an elite corps, using abducted Christian boys (mostly from the Balkans), then raised and trained in the Ottoman empire to form the Janissary units. It started out like that at least, after a few hundred years they were more like a social class of their own, with all the corruption that goes with it. And abducted Christian boys were no longer the vast majority of recruits.

The notion of young slave boys pressed into specific military service is of course very Unsullied. And the fact that the Unsullied are eunuchs also ties in with the Arab/Middle Eastern practice of employing eunuchs in various functions, though afaik none of these were military in nature.

It has to be said that the historical Janissaries were not forcibly castrated or anything.

The historical Janissaries were undoubtedly not the only warrior group to use slave boys, I'm sure. But it's the one I immediately thought of.