If the difference between two numbers is 6 and the difference between their squares is 60, what is the sum of their cubes ?

520

The difference between 2 numbers = 6 

We know that,

a² - b² = (a - b)(a + b) 

Let two number be a and b

According to the question,

a - b = 6      ----(1)

And,

a² - b² = 60

= 60 = (a + b)(a - b)

= 60 = 6(a + b) 

= (a + b) = 10      ----(2)

From (1) and (2) get,

a = 8, b = 2 

Sum of their cube = a³ + b³ = 8³ + 2³ = 512 + 8 = 520