The only other components are a 7805 5V voltage regulator, 2x100nF decoupling capacitor, 16 resistors, an IR receiver and a single PIC 16F88 microcontroller. Many other LED cube projects use all sorts of shift register chips etc to perform their addressing of the LED matrix.
To save on component and wiring effort it makes use of the charlieplexing addressing technique previously described in instructables:
previous projects using this are:
I'd recommend reading at least the first two before continuing to read this instructable.
Step 1: Strip the LEDS from a string
Strip and unsolder all the leds in the string.