Huge Rubik Cubes

YongJun MoYu 13 Layer, made in China, 2015.
(plastic, 5+1/4", over 1000 pieces, weighs 5+1/3 pounds)

This cube goes improves the 11x11x11 design with extra tabs on the ends of some pieces. Tony Fisher does an impressive job in a video showing a complete disassembly of the cube, and a second video showing a reassembly; he identifies 38 piece classes.

Even larger Rubik's cubes have been custom made with 3D printing. In February 2011 Oskar Van Deventer presented a Rubik 17x17x17 cube called "Over The Top" (using Shapeways 3D printing technology), In 2016 Coren Puzzle made a 22x22x22 cube), with 2,691 pieces, and in 2017 Grégoire Pfennig demonstrated this 33x33x33 cube with 6,153 pieces (and 6,534 stickers):

The reduction to a Rubik 3x3x3 solution used for Rubik 4x4x4 and Rubik 5x5x5 solutions can be used (in principle, with enough patience) for solving large cubes of any size.

Further Reading
Tony Fisher Disassemble,, from:
Tony Fisher Reassemble,, from:
Deventer presentation February 2011, from:
Shapeways Page, from:
Rubik 17x17x17 Video, from:
Rubik 17x17x17 Disassembly Video, from:
Ruwix Page about the 22x22x22 cube, from:
Ruwix Page about the 33x33x33 cube,, from:
Greg's 33x33x33 video,, from: