For some time I have talked about building an LED cube and have finally got around to building one.  The cube is electrically arranged as 8 layers of common cathodes and 64 columns of common anodes. 

The processor used is a Microchip dsPIC33FJ128MC802.  This is really overkill for such a simple device, but is one that I had available to use.

The 64 columns are driven by 8 CMOS shift registers controlled by 8 output bits from the processor.  The 8 layers are driven by 8 transistors controlled by another 8 output bits from the processor.