This is a fractal thing that can be iterated n number of times in the SCAD file. The cube on the stand prints without support at any size, and, if left unscaled, the stand is easily removed for a well-printed cube.
The Sierpinski cube/menger sponge that has been rotated and put on a stand was designed by BBO, whose thingiverse account is here:
http://www.thingiverse.com/bbo/about
The pictures of the different cube builds are also thanks to BBO.

BBO also uploaded a sprued version of the cube (at n=3) so that it will be easy to print and cast in metal. That can be found here:

http://www.thingiverse.com/thing:535927

If you're so inclined.

--Printing tips--

-Be conservative with your shells and infill amount when n>3.
-The cube can be printed without support, but the larger your cube is, the more likely it will need support to look nice.

Please comment with any problems you experience/suggestions you have for improvement.