We believe this Instructable is the most comprehensive step-by-step guide to build an 8x8x8 LED Cube ever published on the intertubes. It will teach you everything from theory of operation, how to build the cube, to the inner workings of the software. We will take you through the software step by step, both the low level drivers/routines and how to create awesome animations. The software aspect of LED cubes is often overlooked, but a LED cube is only as awesome as the software it runs.
A video is worth a thousand words. I'll just leave it up to this video to convince you that this is the next project you will be building: