And, unless you offer money, I doubt he'll give it back. You made the mistake of trading something, now you must live with the fact that the only way to get the puzzle back is to buy a new one. I know how this feels, I did the same thing with some Lego minifigures. I traded them, then regretted it. Its been years, and I still miss those Legos, but will never ever ask for them back. The only way you should do this is to say your sorry, that you regret the trade, and you'll trade him back the cube he gave you (or something better). Other than that, you must leave it be, and just buy a new cube. Its sad, but, something we must move on.
Sorry if this was mean or unhelpful, but this is how these things work.