Been there, done that.
If my main aim was to do that then I'd use a Raspberry Pi. You even get hardware OpenGL.
...or scripts, effect files or whatever you can dream up.
I'm more worried about how dim they'll get under heavy multiplexing. Maybe I can up the current a bit to compensate, most LEDs can lake 100mA with a low PWM duty cycle.
Another option is be to latch them all using banks of serial to parallel chips but that's a lot more hardware.
I was more worried about brightness, even with a 4x4x4 cube the LEDs will only be on for 12.5% of the time (assuming eight output lines).
Good point, I hadn't thought of that...
A lot of the projects use a serial-to- parallel chip for the data outputs so you only use three Arduino pins for that. The rest of the pins are used to select blocks of 8 LEDs in the matrix.
Depends on the controller...
Arduinos usually run at 16MHz.
Yep. Parts are hard to get where I live so I buy lots of stuff on eBay.
eBay sells big 8x8 LED arrays quite cheap. Some of them connect together like Lego so you can build big displays.