Cube the coefficient of each variables.
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Do the inverse operation. Given is product, so look for the quotient which is the other factor.

  \frac{27x ^{2}-64y ^{2}  }{3x-4y}

The result:  9x² + 12xy + 16y² is a perfect trinomial  which can be factored as
(3x + 4y)².

Therefore, the other factor of number to be multipled to (3x-4y) is (3x + 4y)².

So that:
(3x-4y) (3x+4y)² = 27x³ - 64y³