2021 Fall AMC 10B Problem 24

A cube is constructed from 4 white unit cubes and 4 blue unit cubes. How many different ways are there to construct the 2 \times 2 \times 2 cube using these smaller cubes? (Two constructions are considered the same if one can be rotated to match the other.)

(\textbf{A})\: 7\qquad(\textbf{B}) \: 8\qquad(\textbf{C}) \: 9\qquad(\textbf{D}) \: 10\qquad(\textbf{E}) \: 11

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.