Rubik’s Cubes seem to have been most popular in the 1980s, but never really went away. As such, if you have one lying around your house unsolved, why not ‘simply’ construct a machine to do this for you?
One possibility is the Q-Bot, outlined here. While it won’t break any world records, it’s a solid-looking assembly that appears to be relatively easy to build.
The Q-Bot features six NEMA 17 stepper motors, four of which turn one face at a time. When needed, the other two use timing belts to alternatively pull opposed stepper motor pairs back, allowing the other two to rotate the entire assembly. An Arduino Mega is utilized to control the steppers via a custom shield, with a computer running the Kociemba’s Algorithm.