Cube
Solder the cube together in layers, the cathodes should all be connected in each layer, the anodes connect in columns. This way, we can turn on each LED individually by setting a column (+ pin) to high and the layer of the desired LED (- pin) to low.
Gotta be careful when soldering, it turns out that LEDs can be destroyed by the heat if you take too long to make a connection.
One of the problems with connecting the LEDs up like this is that we can't turn on two LEDs in two different layers without also turning on the LED in the corresponding column and layer. To get around this, anytime we turn on multiple LEDs we need to turn them on and off really fast one by one, this way, we can have any group of LEDs appear to be on while the rest are off.
Make sure you test after you use the soldering iron, if one of the LEDs dies it's A LOT easier to replace it now rather than when the cube is finished.
Apologies for the potato quality.