"wouldnt turning on group 1 section 1 turn on that whole section? not individual LEDs?"
Only if the anodes were driven high for all LEDs. Otherwise, just the LEDs with High anodes turn on.
The idea is you enable 1 group of 5 LEDs at a time, a 5x5x5 cube would have 25 groups to cycle thru. 4% duty cycle.
Driving each group for 1667microseconds would yield a 24 Hz refresh rate - leaving over 25,000 cyckes in between writes to do other stuff.
I would imagine a loop within a loop to cycle thru the groups & layers, reading from a 25-byte array (upper 3 bits ignored) to send out a new byte every 1667uS. 2nd array of 5 keeps track of group enable pins, 3rd array of 5 keeps track of layer enable pins.
There are 5 anode drive pins, 5 group select pins, 5 layer select pinsl, so the whole cube is multiplexe with just 15 pins, directly controllable by a single '328P chip with no extra shift registers. Just 15 resistors and 20 transistors.
I didn't make one myself, just helped the original requestor with a design that could be done.