Or how common was it throughout its history? And which cities outside Sparta were keen to send their sons to the agoge? I was reading somewhere that apparently the rich families of other cities viewed it as a status symbol to have sons participate in the agoge and vied for the chance to do so.
This doesn't quite match up with how the Spartans viewed themselves compared to other non-Spartans and so the idea of non citizens participating sounds odd, but still, it's possible right? I can't find the source which mentioned this so
I can't speak for instances of other Greeks participating in the agoge, but I can at least give you a partial answer. Your post made me think of the mothakes (Doric Greek for "stepbrothers"). Essentially they were male members of Spartan society who participated in the agoge and existed outside the privileged homoioi class. They were permitted to fight, however, I'm not quite sure of the extent of their social limitations. There were different individual circumstances, but generally they were the children of poor/disgraced families or the bastards of Spartan father's and Helot mothers. Some Spartan commanders (most notably Lysander who defeated the Athenian fleet) even came from this underclass of the Spartan hierarchy and rose to prominence.