
1) Offer encouragement
There is no solution. This is an impossible puzzle."
Eddie Moya "You can do it!" Richard Simmons 3) Suggest a scientific conceptthat could hold the key to solving it (i.e. dark matter, gravitational waves, instant rice, time dilation etc)
"Take advantage of gravitational redshift by throwing the cube into a black hole. Eventually, all sides will appear red, and thus, solved." Alison McDonough 
2) Develop an engineering solutionCreate an invention, a robot, an algorithm, or schematic of a device solve it. Send images to boob@movingpartsllc.com
4) Other theoriesOther theories, physical or metaphysical, mathematical, computational, philosophical or practicable that you think have potential.
"The solution becomes obvious once we assume that the cube is massless and in a vacuum."  Jason Hempstead 

Scientists will neither confirm nor deny that the reason they created the Hubble Space Telescope was to look for the solution to the Boob Cube.

The universe on the grandest scale we know. What about dark matter? What about Boob Cubes? Nobody knows.

This is a 3D plot of fermionic condensate. There is a great deal of science data contained in this .jpeg that may prove useful.
