The perfect cubes less than 1000 are:
1^3 = 1
2^3 = 8
3^3 = 27
4^3 = 64
5^3 = 125
6^3 = 216
7^3 = 343
8^3 = 512
9^3 = 729
so
2^3 = 8 could only be 1 + 1, but this is 2, not 8.
3^3 = 27 could be 1 + 1, 1 + 8 or 8 + 8, but all of these are too small
4^3 = 64 could be 1 + 1, 1 + 8, 1 + 27, 8 + 8, 8 + 27, 27 + 27.
general proof that a^3 + b^3 = c^3 holds for no positive integers
hope it helps
