Solution
Given, $$a + b = 27$$
$$a^3 + b^3 = 5427$$
$$=$$> $$\left(a+b\right)\left(a^2+b^2-ab\right)=5427$$
$$=$$> $$27\left(a^2+b^2+2ab-3ab\right)=5427$$
$$=$$> $$\left(a+b\right)^2-3ab=201$$
$$=$$> $$\left(27\right)^2-3ab=201$$
$$=$$> $$729-3ab=201$$
$$=$$> $$3ab=729-201$$
$$=$$> $$3ab=528$$
$$=$$> $$ab=176$$
Hence, the correct answer is Option C
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