Waring's problem for cubes

Waring's problem for cubes : Every positive integer can be written as the sum of nine (or fewer) positive cubes.

6 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3

7 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3

8 = 2^3

9 = 2^3 + 1^3

10 = 2^3 + 1^3 + 1^3

11 = 2^3 + 1^3 + 1^3 + 1^3

12 = 2^3 + 1^3 + 1^3 + 1^3 + 1^3

13 = 2^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3

14 = 2^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3

15 = 2^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3

23 = 2^3 + 2^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3.

24 = 2^3 + 2^3 + 2^3

29 = 3^3 + 1^3 + 1^3

31 = 3^3 + 1^3 + 1^3 + 1^3 + 1^3

51 = 3^3 + 2^3 + 2^3 + 2^3

Based on this, is it reasonable to suppose that every integer is the sum of nine positive cubes (or fewer) ?

23 is written as the sum of nine positive cubes. Can you find other numbers which can be written as the sum of nine positive cubes?