A LED cube is like a LED screen, but it is special in that it has a third dimension, making it 3D. Think of it as many transparent low resolution displays. In normal displays it is normal to try to stack the pixels as close as possible in order to make it look better, but in a cube one must be able to see trough it, and more spacing between the pixels (actually it's voxels since it is in 3d) is needed. The spacing is a trade-off between how easy the layers behind it is seen, and voxel fidelity.
Since it is a lot more work making a LED cube than a LED display, they are usually low resolution. A LED display of 8x8 pixels is only 64 LEDs, but a LED cube in 8x8x8 is 512 LEDs, an order of magnitude harder to make! This is the reason LED cubes are only made in low resolution.
A LED cube does not have to be symetrical, it is possible to make a 7x8x9, or even oddly shaped ones.