Hey gammerx, most led cube projects use multiplexing to control the LED. No two Led's are ON at the same time. They are just being refreshed very quickly, and the eyes get fooled into believing that they are all on at the same time. Look into Persistence of Vision (POV) to learn more about this. The Gyro part of it is not to bad ones you get the multiplexing down. In-fact, for your project, I think you would be better off with an Accelerometer since all you need is the cubes orientation. Gyros are used for Angular Velocity.
Jay