The Japanese cube is one of a very few true three-dimensional weaves. It is solid and can be used for sculpture, although it is highly ring-intensive. To keep its shape, it requires very small rings, so small, in fact, that it's usually easier to simply double up the rings. For example, good cubes can be made from doubled 1/4" ID 16 gauge rings, or doubled 3/16" ID 18 gauge rings, but they can also be made from single 16 gauge 1/8" rings. It is important to note that the Japanese cube, unlike its two-dimensional relatives, works best with only one ring size.
For these instructions, copper rings are horizontal, and silver rings are vertical.

Step 3: Add nine horizontal links. This completes one layer of the cube - each layer has two rows each of horizontal and vertical rings.

Step 4: Another set of vertical links passing through horizontal links.

Step 5: And even more horizontal links. By this point the pattern should be obvious.

Step 6: Continue following the pattern until you've finished the cube.

Et voila! One Japanese cube. Of course, they don't have to be 3x3 - you can build them to any size you like and any dimensions.