(I) Consider two positive integers x and y with x < y < 2011 and, determine the minimum value of a positive integer constant n satisfying: x^{3 } + y^{3 } = 2011^{3 } + n
(II) Keeping all the other conditions in (I) unaltered, determine the minimum value of n satisfying: x^{3 } + y^{3 } + n = 2011^{3}