Warning, spoilers ahead:
The color ring is an interesting model with a few different solutions. Below is how I solved it. Notice I have four solid bodies in the feature tree. I think some other solutions ended with a single solid body.
Sweep, color, pattern
The main trick is getting the model to build with seams so the colors can be applied. The image below should make the Sweep profile easy to understand. It is a "circle", but it has been split, or otherwise drawn with four arcs. This creates the seems. The path is another arc representing 90° of rotation.
The final circular pattern should need no explanation, but if you color the model first, then enable the Propagate Visual Properties option, you'll only have to apply half the colors.