Play in New Game+ mode and enable the "Flight mode" code when meeting the Hexahedron. You can move as it but will be taken to another screen with the Black Monolith in first-person after completing the view rotation tutorial it provides. The text translates to:
After collecting all 64 Cubes, go back through the Star Gate in the 32 Cube room for a different ending. After the credits, select New Game + again from the main menu. When you reach the part where you usually receive the Fez and the Sunglasses, you will instead get a pair of red/blue 3D glasses. These automatically enable Stereoscopic Mode, which be disabled in the Settings menu should you not want to use it.