That can't be true either since -91 = (-3)^3 + (-4)^3 and -91 = 5^3 + (-6)^3. Since -91 < 91, the statement has to be false.
In fact, it is not the number x with smallest value |x| that can be expressed as the sum of two cubes in two different ways since, 0 = (-1)^3 + 1^3 and 0 = (-2)^3 + 2^3.
It appears that 91 is the smallest positive integer that can be expressed as a sum of two cubes in two different ways.
There is no value to this comment. I mostly just wanted to be annoying. I hope I'm right, at least.