a.k.a. V-Cube 7x7x7
Patented by P. Verdes 2007, made by V-Cube 2008.
(plastic, 3.1 inches;
opposite black is yellow, opposite red is orange, opposite blue is green)

This cube has a slightly bulging shape. The V-Cube 7x7x7 on the left is described in the same patent as the V-Cube 6x6x6 (the patent describes designs as large as 11x11x11), and like that cube, it uses slightly rectangular cubes on the edges and larger square cubes at the corners (the 7x7x7 has continuous action, whereas the 6x6x6 has click stop action).

The reduction to a Rubik 3x3x3 solution used for Rubik 4x4x4 and Rubik 5x5x5 solutions can be used for solving this cube.

Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/cube7.htm
Wikipedia Page, from: http://en.wikipedia.org/wiki/V-Cube_7
Verdes Patent Application, from: www.uspto.gov - patent application 2007/0057455
Verdes Patent, from: www.uspto.gov - patent no. 7,600,756