A few years back I built a couple of 4x4x4 L.E.D. cubes, one using 3mm red L.E.D.s and the other using tiny surface mount L.E.D.s (1206 or 0805).
The first was the 3mm version using an Atmega32p.
It has a lot of animations. I tried to make videos showing most of the animations.
The second cube is made of tiny surface mount LED’s soldered to single stands of copper wire from solid strand cat5 cable and is powered by an Arduino Pro Mini 168. It runs all the same animations as the larger one above.
The videos only show a couple of the animations.
The code can be found here: https://github.com/Intrinsically-Sublime/4x4x4_LED_Cubes