Consider the equation: X^{3} + Y^{3} = Z^{3}, where
(i) Each of X and Y is a positive integer and
(ii) Z is a real number such that Z^{3} is a positive integer, and:
(ii) The four digits immediately following the decimal point in the base ten expansion of Z are 2, 0, 1 and 6 (in this order)
Find the three smallest values of X+Y