For that scenario to be the case then it is either thousands of years in the future and someone fancied having a bit of fun, or physics as we know it (things tending to go for the lowest energy state for starters) would need to be radically rethought.
Going on from there and assuming the material holds together and does not slump back to spherical we get to consider the effects of things. I am not sure what size this cube would be but as most physical effects scale with distance, area or volume then the variability of a cuboid compared to what is essentially a spheroid (difference of a face length of a cube vs that of extreme diagonals, now compare to a spheroidal object which... is the radius basically wherever you look). Gravity would be one of the first things to consider and would probably trouble satellites considerably.
The axis of spin would also want to be considered here as it would have effects upon the light received for the sun, and possibly shadows cast. An example now would be the temperature of the poles which are effectively further away from the sun at any given point.
Speaking of slumping back to spherical we would probably also see any free flowing items drift away from areas depending upon what the effect of potential energy would be (water does not flow up hill and all that).
So basically everything would likely die.