AMC 12 2020b Problem 20

Two different cubes of the same size are to be painted, with the color of each face being chosen independently and at random to be either black or white. What is the probability that after they are painted, the cubes can be rotated to be identical in appearance?

\textbf{(A)}\ \frac{9}{64} \textbf{(B)}\ \frac{289}{2048} \textbf{(C)}\ \frac{73}{512} \textbf{(D)}\ \frac{147}{1024} \textbf{(E)}\ \frac{589}{4096}