Yeah, like some others said, the administrators hear all day long about "I didn't know" or "I didn't do it" although it is plain that they did.
They are looking for maturity. The mature thing to do, is say this.
"I have to say that what I did was wrong. I didn't think so before, but have realized that it is now. I want to take this opportunity to apologize
to my teacher and to you. I accept any punishment that you deem appropriate for me. Again, I am sorry."
Short, sweet, and a mind blower for the administration.
They will be impressed that you accept responcibility and respect that. They might even go easy on you since you "learned your lesson"