The difference between two numbers is 5 and their product is 14. Find the difference between their cubes.

Let the two numbers be x and y.

So,

x - y = 5

And,

xy = 14

Using the formula,

[∵ (x - y)³ = x³ - y³ - 3xy(x - y)]

So,

⇒ (x - y)³ = x³ - y³ - 3xy(x - y)

Putting the value (x - y) = 5 and xy = 14, we get

⇒ (5)³ = x³ - y³ - 3 $\times$ 14 $\times$ 5

⇒ 125 = x³ - y³ - 210

⇒ x³ - y³ = 125 + 210

⇒ x³ - y³ = 335

Hence, the difference between their cubes is 335.