"I'm sorry for being later." is correct, but I guess you mean "I'm sorry for being late.".
"I'm sorry for late" is incorrect.
You can either say "I'm sorry for <verb>." or "I'm sorry for <noun>."
In noun form, you can say: "I'm sorry for my lateness."
In verb form, it's <verb>ing, which is why you can say: "I'm sorry for being late."
Or you can say "I'm sorry that I am late."
Some other examples are:
"I'm sorry for moaning." [verb]
"I'm sorry for the delay." [noun]
"I'm sorry for what I said."