In May 2005, the Greek Panagiotis Verdes constructed a 6×6×6 Rubik’s Cube. and on May 23 2006, Frank Morris, a world champion Rubik’s Cube solver, tested this version. He had previously solved the 3×3×3 in 15 seconds, the 4×4×4 in 1 minute and 10 seconds, and the 5×5×5 in 1 minute and 46.1 seconds. The 6×6×6 took him 5 minutes and 37 seconds to solve. Morris himself thanked the inventor for making it and purportedly stated that the bigger the Cube is, the greater the pleasure. In July 2006, Mr. Verdes successfully constructed the 7x7x7 cube, and on October 27 2006, a video of Frank Morris testing the cube was released. Morris solved the puzzle in 6 minutes and 29.31 seconds. Videos of these tests can be viewed at http://www.olympicube.com/.

In 1994, Melinda Green, Don Hatch, and Jay Berkenilt created a model of a 3×3×3×3 four-dimensional analogue of a Rubik’s Cube in Java, called the MagicCube4D. Having more possible states than there are atoms in the universe, only 55 people have solved it as of January 2007. In 2006, Roice Nelson and Charlie Nevill created a 3×3×3×3×3 five-dimensional model. As of January 2007, it has been solved by only 6 people.

Here is a good video of the 7×7.
http://www.olympicube.com/video/7×7.html