Animations with all colours
Mathematica
This is a straightforward implementation with each rgb colour occupying an intersection in a 256 by 256 by 256 unit grid.
The jerkiness seems to be an artefact of the video, not an error in the data, which should be exact.
red values increase downwards, green values increase rightwards, and blue values increase by frame.
Perhaps I'll jumble things up later.
f@b_ := Image@Table[{r, g, b}/255, {r, 0, 255}, {g, 0, 255}]
Export[&quot;c.mov&quot;, Table[f@b, {b, 0, 255}]]

QuickTime clip