Is it okay to tell an ex who tries to contact you that you are aware that they cheated on you?

The last time me and this person spoke we were on good terms and they vanished because they were “going through something” only for me to later find out that they had started up a new relationship with another girl. To add insult, they never once mentioned anything to me about wanting to date someone else and had even heavily implied as well as flat out told me that they wanted to be with me-even cried in front of a group of their coworkers in a busy club about still being in love with me and wanting a second chance to get it right. But when I found out the truth, I knew that they basically left me for somebody else even though they never told me. Years later the person messages me asking for forgiveness and I say “I accept your apology” and then cease any further conversation. Perhaps because I was kind enough to accept their apology for “what they did in the past” as they vaguely put it, or because they are unaware that I know the truth, they continue trying to reach out to me to talk. I honestly want to tell them that I know what they did and That the fake love they had for me has been exposed. I want them to know that I am aware of the fact that they were pretending to be in love with me. I have only ignored their attempts to start conversation rather than blocking them because I have honestly felt tempted to let them know that I know what they did. But I feel like deep down something in me doesn’t agree with the idea that I should confront them. I don't know why I feel like that but something tells me that confronting them is more trouble than it’s worth to just flat out block them. So I’m torn between confronting him finally now that he is so adamant to by in touch with me or just blocking him and moving on without ever telling him my true feelings. I don't know which choice to make
Is it okay to tell an ex who tries to contact you that you are aware that they cheated on you?
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