Here is my plan for a 4x4x4 LED cube utilizing the Max7219 IC as a multiplexer. It uses SPI, so it requires very few pins on the microcontroller to operate. I ordered the parts from ebay last night. I already have 64 green LEDs.
It’s using a 7-segment display driver. Since a 7-segment display also has a decimal point, I have 8 total individually addressable LEDs per “digit” for a total of 64 LEDs...just right for my 4x4x4 contraption. There are plenty of YouTube videos describing how to assemble something like this, but only two mention the Max7219. [One of those](https://www.instructables.com/id/JolliCube-an-8x8x8-LED-Cube-SPI/) is an 8x8x8 cube (it uses 8 Max7219 chips), far too much soldering for me right now. 64 will be bad enough. The [other](https://www.instructables.com/id/Led-Cube-4x4x4-With-Max-7219/) is extremely difficult to understand, so I came up with my own design.
The “digit” identifiers are for addressing the Max7219. They are connected to the common cathode for the digit. The layers will be soldered together so that the anodes of similar letters will be stacked. I’m already thinking of how such a thing would be programmed for animations.
There are libraries [out there](http://playground.arduino.cc/Main/LEDMatrix) that allow you to address an LED matrix using the Max7219 by rows and columns, so I'm going to wrap one of those and add my own methods for dealing with the layers.