If $$a^3 - b^3 = 2349$$ and $$(a - b) = 9$$, then $$(a + b)^2 - ab$$ is equal to:
$$(a-b)=9$$.............(1)
$$(a-b)^3=729$$
$$a^3-b^3-3ab\left(a-b\right)=729$$
$$2349-3ab\left(9\right)=729$$
$$27ab=1620$$
$$ab=60$$..............(2)
$$(a-b)=9$$
$$(a-b)^2=81$$
$$a^2+b^2-2ab=81$$
$$a^2+b^2-2\left(60\right)=81$$
$$a^2+b^2-120=81$$
$$a^2+b^2=201$$..........(3)
$$(a+b)^2-ab=a^2+b^2+2ab-ab$$
$$=a^2+b^2+ab$$
$$=201+60$$
$$=261$$
Hence, the correct answer is Option C
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