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If he started dating this new girl A WEEK after you guys broke up, he was most likely talking to her before you guys broke up. Sounds like he's talking to you & sexting because either you were available to do so, and sometimes people act on opportunity instead of feelings.
He may be ignoring you now because he regrets doing that to the new chick behind her back.
Either way, like the other posters said.. Just cut off all contact & block him.. You'll get over him faster & you won't get any drama from his new chick if she finds out about the flirty texts between you guys.