60 x 60 x 60 sounds a bit small to me for a kitten to be locked in all day to be honest.

My 2 cats sleep in my room in a massive cat/dog crate. They are only in their at night and have free roam of the house all day, apart from when no one is home to watch out for them... which is very rare. There's always at least someone at home here during the day.

If my situation was to change, and they had to be left alone for a good few hours during the day... I wouldn't "lock" them in their crate, I'd probably kit a room out for them to have free roam of.