I have not included the program to make the LED cube light up because its a work in progress. The program is the hardest thing to put together because I am just starting to learn the Arduino software. All ready made programs can be found on the internet but making your own is what its all about. I will update this instructable with the finished program as soon as it is finished.
The paragraph below, describes how the circuit works which may or may not make it easier to write a simple program to turn the LEDs on and off.
How it works: Basically, a pin from the arduino is connected to the LED anode and a different pin is connected to the base on the transistor. The controller is then connected to the LED cathode and the emitter is then connected to ground. When the pins for the base and LED anode are turned on this causes current to flow through the LED. Thus turning it on. A great way to turn it on and off is to keep the base pin "on" and turn the anode pin "on" and "off". A great website that illustrates how the NPN transistor works is http://www.falstad.com/circuit/e-npn.html.