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1. $a^{3} - b^{3} = 513$

Answer: Option A

Explanation:

a^{3} - b^{3} = 513 \Rightarrow {(a - b)}^{3} + 3 a b (a - b) = 513 \Rightarrow {(3)}^{3} + 3 \times a b \times 3 = 513 \Rightarrow 27 + 9 a b = 513 \Rightarrow 9 a b = 513 - 27 \Rightarrow a b = \frac{486}{9} = 54

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