If a³ - b³ = 513 and a - b = 3, What is the value of ab?

Question: If a³ - b³ = 513 and a - b = 3, What is the value of ab?

Solution:
given,
a³ - b³ = 513
a - b = 3

we know that,
a³ - b³ = (a - b)³ + 3ab(a - b)
or, (a - b)³ + 3ab(a - b) = 513
or, 3³ + 3ab(3) = 513
or, 9ab = 513 - 27
or, ab = 486/9
∴ ab = 54