This step largely follows the LED Cube 4x4x4
but we'll be building a 3x3x3 cube instead. A cube of this size is about as big as it gets without introducing additional circuitry and complexity. We'll need a total of 27 LEDs that will be grouped into three sets of nine.
Each set of nine LEDs will share a common connection amongst their cathodes (negative leads). I'll refer to each of these sets as a "level". Each of the nine LEDs on a level is connected to the corresponding LED on the other two levels through their anodes (positive leads). These will be referred to as "columns". If that didn't make sense it will become self explanatory as we build the cube.
To start we'll use a drill to create a jig out of a small piece of scrap wood. The jig will hold the LEDs in place while we solder them. I decided to space the holes around 5/8 of an inch apart (~15 mm) but the exact distance isn't critical. The hole should have a tight fit around the LED since we don't want them to move around while soldering.
Once the jig is done we're going to bend the cathode of each LED in a 90 degree angle. The cathode is identifiable in three ways: 1) It's the shorter leg, 2) It's on the flat side of a round LED, 3) it's connected to the larger piece inside the LED. Make sure you bend the cathode in the same direction for all of the LEDs.
Now we're ready to begin soldering.