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$$27a^3 - 2\sqrt{2}b^3 = (3a - \sqrt{2}b)(9a^2 + 2b^2 + 6\sqrt{2}ab)$$
($$\because a^3 - b^3 = (a - b)(a^2 + ab + b^2)$$)
here,
a = 3a
b = $$\sqrt{2}b$$
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