My Favorite Unsolved problem: (6)

It is known that the number 3 can be expressed in two ways

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

and also

4^3 + 4^3 + (-5)^3 = 64 + 64 - 125 = 128 - 125 = 3


Can we find other ways to express 3 as the sum of three positive or negative cubes?