They are using the simple program to control the servo motors via Arduino Board. Do you remember the concept of coding the servo motor like (servo.attach(pin), servo.write(angle)) in our expert level?? Even though it is a simple program when putting that program inside of the cube itself, it looks like magic right?
Start building your own Self-solving Rubik's cube by learning the concept of servo motors and how to program it in our Expert Level!!
Source: TheVerge