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.
Step 1: Step 1: Materials
List of Materials
27 leds $7
3 NPN 3904 transistors $3
9 220 kilo-ohm resistors $4
3 22 kilo-ohm resistors $2
wiring kit $10
bread board $8
Arduino Uno $20-$25
soldering iron $9
Total Price: $70, but the learning experience, priceless.
Step 2: Step 2: Soldering the LEDs
Each layer of LEDs has to be soldered separately. To solder each layer, stick the LEDs in the holes and bend down the cathodes to solder all of them to each adjacent LED. After all three layers have been soldered you should have nine anode leads from each layer. Solder each adjacent layer of anode leads to the corresponding layer.
I have included a picture below on how the finished piece is supposed to look.
Step 3: Step 3: Wiring Up the Breadboard
Now connect the three NPN 3904 transistors to the breadboard. The controller and base should be connected to separate strips on the breadboard while the emitters can all be connected to one strip. Connect the emitter strip to ground. Wire a 22 kohm resistor to each base lead and connect to a pin on the arduino. You sholud now have a total of 9 + 3 = 12 pins wired on the arduino. Connect each controller lead to a separate cathode connection on the LED. Each controller should be connected to a different layer.