The actual beat detection is done in hardware by an onboard amplifier and a microphone. On each music beat the microcontroller randomly selects a LED animation pattern which is shown on the 3x3x3 LED grid.
The LED cube is completely autonomous, just place it near an audio source and it will start to glow in sync with the music! :-)
Here it is in action:
For videos and schematic see the project page http://audioledcube.wordpress.com