We've seen N holding a yellow Cube the times you battle with him.What is this cube excacly ?

The cube hanging from N's belt is a sliding puzzle similar to a Void Cube, and has been in his possession since childhood. It's one of many design elements reflecting the character's mathematical motif, and also resembles the first iteration of a Menger sponge, a geometric figure that simultaneously has infinite surface area and zero volume.

http://bulbapedia.bulbagarden.net/wiki/N#Trivia