Here is another Lego cuboid that is more challenging then the 2x1x2 cuboid. It has six cuties with no core, and two rubber bands. It also turns VERY smoothly with loom bands. See step 1 for internals at a closer look into this amazing little cuboid.
Step 1: Internal Rubber Bands
Here you can see the internals of the cuboid. This is just a 2x1x2 basically, with a middle extension.
The extension is two cubes held together by one doubled loom band, because all they will do is rotate on each other. To add the extension, pull the four cubes on the 2x2x1 apart, then place the extension in the middle. Then you would add the top white panels to hold the band in place.
So that is basically it for my new cuboid and I hope you enjoyed it! I may try to work on a 3x3x1 next, I will see. As always just ask in comments for instructions, but I will make some anyways soon. Hope you enjoyed! Cya