Is it obligatory for someone who broke their fast on a number of days in Ramadan, believing they had not yet reached puberty, and then later realized they had indeed reached puberty, to make up those days?

There are three signs of puberty for a male: emission of semen, or the growth of coarse hair around the private parts, or reaching fifteen lunar years of age. If you broke your fast certainly after puberty, then you must repent and make up the days you missed without expiation, because expiation is only required for breaking the fast through sexual intercourse. However, if you broke your fast while uncertain about whether you had reached puberty, then you are not required to make up those days, as the default is not having reached puberty. You must repent from masturbation (self-stimulation), as it is forbidden.