Hi, thank you for all your help! 

I have finished my cube! here are links to some pictures:

https://ibb.co/74dLJZP
https://ibb.co/gtcBGGg
https://ibb.co/k8w6VFB
https://ibb.co/rxLhMXn

Here is a quick video of my cube:
https://youtu.be/98Mnf0n86zM

Next I am going to try making the RGB version like you and Asher made

You're welcome. The key to "hiding" wires are those global labels. They allowed us to connect points without showing the actual wire lines. Yes, all four resistors on the transistor base should be at least 1K, 10K would work too. Thanks for finding that mistake. I've corrected the schematic.

While you CAN use a 16MHz crystal and two capacitors. I used a Ceramic resonator, which basically have those three components in one package. Ceramic resonators are less precise, but for most Arduino projects it is good enough. I've added links to parts including the ceramic resonator below each part in the hackaday post under Components.
https://hackaday.io/project/170607/components

I also have a question about the 16MHz crystal (I know its only needed if I use the stand alone chip). It seems like the crystal in your schematic has 3 pins (and the part might include two capacitors?) where two of the three pins go to the AtMega chip and one goes to ground. The crystal that I'm looking at only have 2 pins. Do I also need to connect capacitors to the crystal?

Hi, thank you for making this project. Looking at your schematic it seems so simple to connect everything. I would have thought there would be wires all over and it would be hard to follow, but your layout is so easy to read! One thing I noticed is that the resistor going to Q4 is 470 ohms whereas the other three are 1k, should they all be 1k?