<p>There is no way that drinking/drug use and cheating can be equivocated in terms of a college application. Colleges accept students for ACADEMIC purposes. Cheating is academically relevant; drinking is not.
Anyway, OP, I would first find out if there’s any way to have the incident removed from your record. If not, you may want to include a note about it in your application; write what you’ve learned. But keep in mind that the odds are not so good.
You may want to read The Gatekeepers; I think I remember there being a discussion of a student who was suspended for a day, wrote her essay about it, had her GC explain it, etc - all in a very positive light. She was still largely rejected.
Good luck.</p>