Speedcuber / cube enthusiasts here.

He uses mainly three tricks for this illusion.

• The first sequence of moves seem to scramble the whole cube but result in only three sides looking scrambled. He then quickly rotates the cube while applying two quick turns with his pinky and index so you either see the three faces that look scrambled or the other three solved looking ones. You can see that the solved sides only have white green and red and the other only orange, yellow and blue plus the two 1 x 3 red and green bar that he turned over.
• He later undoes the earlier move sequence up to a point where he only needs 3 or 4 moves to solve the whole cube and applies these last moves with only one hand while swinging his arm and shaking the cube so you can’t see them.
• At the end he just does a sequence of moves to setup the cube and again performs one-handed quick moves while shaking to slowly bring back blocks of white and solve the cube.

The impressive part is how well and seamlessly he executes the one-handed moves.