Here is my 3x3x3 LED Cube project. It runs using a PIC16F690. Along with the brief explanation of how to make it, I have also included the .asm file for the PIC and a piece of software written in VB.NET that you can create your own LED patterns. These can be exported as .asm files and put into the main .asm code.

http://www.instructables.com/id/3x3x3-LED-Cube/