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Assume a is the decimal portion of (x - \(\sqrt{3}\) y)^3.
Since the integer portion of (x - \(\sqrt{3}\) y)^3 is 0, we have a = (x - \(\sqrt{3}\) y)^3.
If c is the integer portion of (x + \(\sqrt{3}\) y)^3, we have (x + \(\sqrt{3}\) y)^3 = c + b.
Then, we have (x - \(\sqrt{3}\) y)^3 + (x + \(\sqrt{3}\) y)^3 = 2(x^3 + 9xy^2) = a + c + b.
a + b = 2(x^3 + 9xy^2) - c
Since x, y, and c are positive integers, a + b is an integer.
Since we have 0 < a < 1 and 0 ≤ b < 1, we have 0 < a + b < 2.
Thus a + b = 1.
(x - \(\sqrt{3}\) y)^3 = a = 1 - b.

Therefore, D is the answer.
Answer: D