Sometimes my ex keeps texting me, then he ignores me for days. What do you think he is doing?

Me and my ex boyfriend were together for a year. We broke up nearly 6 months ago. He was the one who dumped he, after an amazing holiday and saying that he loved me more than anything, he simply texted me that he wants a break up. Later he said it was because that week he broke up with me he felt like he wasn't in love with me anymore. I tried to talk to him that maybe we could solve things, but he kept saying he wasn't in love with me. He said he didn't understand what happened to hi, that week we broke up, he said he just felt he didn't love me. Then we had a no contact rule for 2 months until December.

This January, I texted him. I felt like I cannot move on and wanted to ask him how he was doing. He said he is fine, has a girlfriend (they got together during our no contact period) and everything is okay. I felt terrible because I still have feelings for him. But, as he said he had someone else, I stopped texting him.

Then he kept saying that we should talk, his girlfriend doesn't mind, that he misses me a lot. He texts me often, says it was awesome to be with me, he doesn't want to lose me, he loves talking to me, and that he is sorry for how he handled the break up. When I asked him did he regret anything, he said no. As there was no point for our conversation, I told him to let's just say goodbye. He then didn't respond at all. After a few days I texted him to please say goodbye with no harsh feelings, then he asked if he could call me later that day, or that week. I told him no. He kept saying he would miss me really much, and he wants to tell me something, but then stopped texting again for days. Now I'm torn whether I should text him again (I feel like I'm chasing him) or block him completely. Whenever he writes those things I start to feel that maybe there is still hope, but then ignores me for days again and I feel terrible. What do you suggest? What do you think of his behaviour?
Sometimes my ex keeps texting me, then he ignores me for days. What do you think he is doing?
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