It is not presently know if for all sufficiently large less than 7 cubes are enough: 8042 is the largest known number which needs 7 cubes and Deshouillers et al. in 2000 conjectured that 7373170279850 is the largest integer that cannot be expressed as the sum of 4 nonnegative cubes.
Every multiple of 6 can be represented as a sum of 4 signed cubes, since
Mahler proved that 1 has infinitely many representations as 3 signed cubes.
Every cube is the difference between the squares of two consecutive triangular numbers .
There is only one known palindromic cube whose base is not palindromic, i.e., 22013 = 10662526601.