8x8x8 RGB LED Cube Project

Hey guys, I am starting up an independent study project for my senior year of high school. I have about a semester to do the project and I am in the planning stages. I am new to Adruino hardware and I was looking for suggestions on what type of Arduino board I should use.
I want to use a Texas Instruments Graphing Calculator as a controller for the arduino hardware, which will then display the function on the cube, much as if you were to press "graph" on the calculator. Any suggestions or information on the materials I may need for this project would be greatly appreciated.

How much are you planning to spend on this?

Any thing less than 100 dollars would be my plan.

That's an ambitious target.

Before you go any further, please try to get 512 RGB LEDs as cheap as possible (as an exercise only). The cheapest ones I could find was about 0.24$ per piece in a pack of 1000.

That is already more than 100$, and we haven't talked about other components, pcb making...

Im not real worried about cost as its a school project, I'm looking for advice on materials that I may need. I already have an arduino UNO, thanks for your help!

Perhaps if you could share with us your largest arduino project to date, we could better determine if our advice is that you should reconsider this project or not.

Keep in mind that a 8x8x8x3(rgb) represents 1,536 active junctions to build and control. That would make me reconsider such a project and I've had significant experiance building electronic projects spread over many decades.

Lefty