If there is any mistake or cheating done by you and you want to apologies for the same, then writing an apology letter will not only show your sincerity but you can also write and clarify what you want in the letter.
In the letter accept the mistake you have done and try to not repeat the mistake in future and assure the same in the letter to the reader.
June 2, 2012
Name/Title Mary Roe
Address 795 E Dragram
City, State, Zip Code Tucson, AZ, 85705
Dear <name>
I am feeling bad about my behavior and want to confess to you that I have done cheating in my project.
I know you hate cheating and don’t accept dishonesty. But as I was out of station for one week, I had no time to complete my project and therefore had submitted my friends projects which is not done by me. I am ashamed for the same.
I hope you accept my apology and give me last chance. I have great respect for you and cannot cheat on you. I assure you it will not be repeated again.
Sorry once again and thank you for your time, hope to hear from you soon.
Regards,
Name