I spent a few hours at the gym on Sunday (or this Sunday). (past)
I'll see you on Sunday (or this Sunday). (future)
You could also say, I'll see you on a Sunday, which means on one Sunday in the future, but not the Sunday that is nearest in time (not this Sunday).
So if you wanted to say that you were born on a particular day of the week, you would say I was born on a Sunday.