Mycroft had never celebrated his birthday.
Gift giving and singing wasn't how things were done in the Holmes' household. They sought reward in their actions and didn't see the appeal in celebrating the first day of one's existence.
Mycroft didn't realise what he was missing out on until his second year of university.
The year he met Greg.
The year he discovered birthday cake.
And the year he received his first birthday present.
Other people must have found this sad, but Mycroft was only pleased that it was Greg who presented him with that very first gift.
He still remembers clearly Greg's uncertain tone saying 'Um, I, er hope you like it. I wasn't sure what to get...'
And even more vividly he remembers the object, as he carries it with him always and admires it daily.