I made this project a few years ago with some classmates in school.
We had some time left in our project week, so we decided to build a led cube.
The microcontroller we used was a 16F648A. The leds are in a 3D matrix.
The cube is divided in 3 rows. These are connected to ground via a transistor. The + of the leds are connected to the pic via resistors.
Video of the LED Cube in action: