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 and in 2017 Grégoire Pfennig demonstrated this 33x33x33 cube:

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: