The two-level Rubik's Cube is simple because it only has 8 corner blocks and no other structural blocks.
There are 8/24=1680 position arrangements for the 8 corner blocks of the second-level Rubik's Cube, and each arrangement has 1107 color directions. That is, after the second-level Rubik's Cube is scrambled, there are (8! 3^7)/24=7!3^6=3674160 states.
The farthest recovery distance of a second-order Rubik's Cube is 11 full rotations, or 14 ordinary rotations. This result can be calculated by a computer using an exhaustive algorithm.
Extended information:
The earliest patent for the second-order Rubik's Cube was applied for by Professor Rubik Alne on March 29, 1983. The U.S. Patent No. 4378117 is what we are used to. It is called the second-order Rubik's Cube of R structure.
Chen Senli of Taiwan's Dongxian Company applied for a second-level patent for another structure on October 27, 1998, U.S. Patent No., US 5,826,871.5826871, which is commonly known as It is a second-order Rubik's Cube of Dongxian structure. There are also some second-level patents for patterns, such as Mickey heads, K-balls, etc.
Baidu Encyclopedia—Second-order Rubik's Cube