So, I got to thinking about a few different things, and I remembered that we never discovered quite what the deal was with N's Puzzle Box. But then, in X and Y we get Shauna, who not only wants to travel across the world, but also enjoys puzzles. Maybe a relation eventually? Or is it just a hope that I'll see N in 3D?

Judging by some concept art, it seems the cube's role was scrapped. Though I think that when Game Freak makes Deep Black and Vast White they'll probably do something, like, putting the Reshiramite/Zekromite hidden inside the cube.

NOPE. it's a menger sponge.

 

A menger sponge is some mathematical thing that has infinite surface area. Fits in well with his name "Natural Harmonia Gropius" since that's a reference to a mathematical sequence with "natural" numbers.

 

and not to mention the theme that plays when you fight against him was greatly inspired by math. lolz.