Most Helpful Guy
Trust is something that is entirely given by the other person.
Speak with him, tell him exactly how you feel (that you cheated, and that you love him and want to regain his trust over time/just had an insincere moment ((you're 21, it can happen))), and it's up to him on whether or not he will let you try and make it up. Don't be mad at any reaction he has (unless it's unlawful or completely inhumane), and accept it. Tell him that you get why he would be hurt and that you're hurting as well (which sounds like the case). Over time, he may come back and give you a shot if he decides to break up with you now. Be patient if you really care for him, and let him know that you'll do anything you can to support and make up for what you did (within reason) and that you care.
Like I said, it's on him. You can be truthful and patient, but he may move on. One thing that I'd like to add is that if he tries to do a "revenge move" like cheating on you back--don't stay with him. That's a character flag and shows that he prioritizes vengeance/his own selfish desires.0