dont know if anyone here knows about glue and plastic, but...
Does a glue based with cyanoacrylate ester attack the plastic in a meffert cube, and in a offical (current one) rubiks cube

I've used it on an original issue Rubik's Revenge. The stickers are so well bonded to the plastic that it will take sanding and delicated paring with a knife to get the stickers off well enough to put new ones.

do you know if the type of glue i have will hurt the plastic? its a crazy glue baesd with cyanoacrylate ester. i use it for modeling

Your best bet would be to dissassembly the puzzle and then test the glue on an interior surface to verify that it won't cause a chemical reaction/problem.