If you're looking for an inexpensive and fun thing to make with your Arduino or compatible board, check out the small LED cube by Arduino forum member "cordes". It's a good starting point for this type of project as the reduced number of LEDs required reduces the complexity of the sketch - and the required construction. Nevertheless it's a fun example and following through the code gives you a solid idea of how it works. In the following video you can see the project in action:
Interested in LED cubes? Coming soon from Freetronics is our new CUBE4: - the 4x4x4 RGB LED cube like no other:
We consider this to be the most versatile, programmable and expandable RGB LED cube kit on the market - and it's coming soon. So stay tuned for the product release announcement!