I cheated on my boyfriend while we were on holiday, I was drunk I don’t even remember it. We live together, should I tell him? I won’t do it ever again.

While being open and honest might seem like the right thing to do, the decision you make should really be based on what you can live with. The ideal situation is that you're honest with your partner about being unfaithful and you work through the issue together. But If you know your partner will be unforgiving, and that coming clean will destroy the relationship, it might be better to keep your guilt to yourself. But can you keep it? Or do you want your own peace of mind? It's your decision. Keep in your mind though that cheating threatens a relationship and hiding it threatens it even more.

the only thing I would ask you is, if he had done the same thing to you and never told you, what would you do and how would you feel? Put yourself in the other persons shoes. Also, the feeling of guilt when hiding something from your significant partner is a terrible feeling. And the longer you wait to tell him the truth, the more problems will arise later for your relationship. If you tell him now there will be a better chance to work it out. But if one day down the road you tell him, he will have even worse trust issues towards you because it took you long to tell him. Also, if he finds out in a different way that you cheated, then that would be terrible. Just put yourself in his shoes and see it from a point of view that is from his eyes.

If you live together it sounds like an important relationship. The effects of being silent and being honest are different. I imagine that you want to express your values but you don't want to lose your boyfriend. I can't advise a route, but it sounds great you don't plan on doing it again, for both of you. Something for your consideration: not remembering something while under the influence of alcohol could be another message for you to make adjustments, quantity and frequency are the key. The effects of a substance is also a feedback to take very seriously, in favor of living with higher quality. My best wishes :)