Question about smokin

Not sure if you mean "caved" as a slang for "gave in," or a typo for "came back" as in "returned to." "Cave back" is not a thing.

You could say "I caved (or gave in) and went back to smoking."

If you are trying to say that you used to smoke, then quit, and now smoke again you could say: "I started smoking again", or "I quit for a while, but now I've relapsed". "Relapse" means that you return to an earlier habit or health condition after having been away from it for a while. In this case, it refers to smoking. On a related note: addictions can be hard to defeat, some people have to try several times before fully succeeding. Multiple *relapses* are not unusual among people who try to quit.

I caved in and went back to smoking. I caved, and smoked. I surrendered to the urge to smoke. I started smoking again. I couldn't quit. I gave up.