This project uses SMD RGB LEDs as the surfaces of the cube which is different from other common LED Cube projects.

The LEDs are placed as shown in the figure below, and the pins at each corner are soldered together (the other side of the cube is same).

By using well-known Charlieplexing technique, switching IN/OUT mode of the pin, we can light one face with full-color capability while the others aren't lit.
Repeating this face-wise rapidly, all the 6 faces of the cube can be independently illuminated by only 8 pins :D