It happened when I intentionally breached the confidentiality provision in my employment contract (big trouble I know) therefore, my boss decided to issue me a warning letter, of course this letter was indicating the "severe damage" and bla bla bla.
I got the letter and acknowledged its contents (and of course this letter is now resting in peace in my employment file), well, my question is, should I write a formal apology letter to my boss and the HR manager, or what is the appropriate action in kind of situations.

Thanks,

I would just let it be forgotten if possible and show them by not doing it again, and by doing a good job.