It's just a question of picking a suitable mod.
The cubes, mod9 are worth {0,1,8}, so any two taken together are worth {0,1,2,7,8} mod 9.
Since the cubes mod9 are worth {0,1,8}, a number that's 4 less than a cube is worth {4,5,6} mod 9.
So the sum of two cubes can never be 4 less than a cube.
Or 5 less, in case anyone is thinking of asking.
Edited on April 5, 2015, 9:50 pm

Posted by broll
on 20150405 21:16:00 