The issue is that each term n^3 equals +1, 0 or -1 mod 9. (Test the numbers 0-9). When you add three of these values, you can't get 4 or 5 (mod 9). Thus, you ca

The issue is that each term n^3 equals +1, 0 or -1 mod 9. (Test the numbers 0-9). When you add three of these values, you can't get 4 or 5 (mod 9). Thus, you can't get a result that equals 4 or 5 mod 9.