Consider the equation: X³ + Y³ = Z³, where

(i) Each of X and Y is a positive integer and

(ii) Z is a real number such that Z³ 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