First trick - The cube has been moved a few times to make it look scrambled completely. He performs a few demo moves (as you can see by the green bar on the D face) which leaves the cube with three solved faces and three scrambled faces. By flipping the cube he shows you only the white, green and red faces to be solved, because the rest is scrambled.
If you watched this live, after a few seconds of awe you would ask him about the other three faces. However, by pointing to the floating cube he distracts you, and you forget about the first cube and completely miss the fact that you only ever saw three faces.
Second trick - Bit more obvious. Either the cube is caught by someone above him and a solved one is dropped (the cube appears to fall back down very fast after he threw it up) or he switches the cube whilst it's off screen down at the bottom.
Evidence for trick 2:
He has a table in front of him. He wouldn't just drop the first cube on to the floor, so he must have placed it on to a table. This strongly suggests there was a second cube that could have been switched whilst the cube was off screen.
Also, there must have been something above him, as the cube in the corner could dangle there. This strongly suggest that someone above him caught his first cube and dropped a second, solved cube down.
Source: I used to be into magic before I started cubing.