My ex cheated on her new boyfriend with me. and she lend me to believe that we had something special, now she pushed me away so she can be with him and one more time she broke me. should i tell him?

No, I don't think you should tell him. I think it is important, however, to speak to your ex-girlfriend. She should know that it was very hurtful that she did, and that you hope she will do better next time. This will give you closure of the event so that she won't be on your mind all the time. There are other ways to get closure, but facing her about it is the best way. If you don't get closure, she will probably be on your mind for a long time, and this will never make you able to move on and forget about her. So you should talk to her, not him. Talking to him will probably ruin their relationship because regardless of how horrible she has treated you, telling him about the bad things she has done will only ruin their chance at a happy life together.

Being cheated by someone is sad. That girl is a terrible person but in my opinion, you don't have to tell him. Let them live their life. But one thing I think you should do is just go and tell her to treat that boy better so that he won't be like you. Tell her that you can forgive her but others don't. And you have to know that, when someone does a bad thing, they will receive karma in the future, sooner or later, it will come. So you don't have to do anything. Forget all about her, and live your life. When you do that, your future will be brighter.