Cyberglitz - Dissected Cube

The main value to me of slicing the color cube into layers is the perspective it provides on where the desaturated colors are.

Deep in the guts of the cube at the very center lives medium gray. Everything else is a color ramp to the outside (surface) where the fully saturated colors live. That is, except for the "spine" which runs from the black point to the white point and forms the gray scale.
You'll find a great perspective on the gray scale "spine" in the Dissected Cube animation.

If you're not sure what desaturated colors are, Check the discussion of Color and HSB in the Color Primer.

If you'd like the slices to hold still so you can examine them, look at the Color Ramp animation. Also the Browser Safe Colors topic in the Primer has one that's slightly different.