Ex won't stop texting

Last month I broke up with my bf , He then got a new gf but I guess they broke up and now he's texting me again saying that he loves and misses me and even asked if he could set his profile pic as a old photo of us which I said no to because it would be weird , I've tried being nice to him but now I'm getting sick of talking and seeing his messages come up on my phone , I know I can block him but I don't want to in case he starts saying stuff that isn't true, I don't know what to do , after we broke up we stopped talking which I was glad for but just out ifnth blue yesterday he texted me.... Just getting really annoyed.