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

Let the two numbers are a,b

Difference between two numbers = 6

$$=$$>  $$a-b=6$$ ...........................(1)

Difference between their squares = 60

$$=$$>  $$a^2-b^2=60$$

$$=$$>  $$\left(a+b\right)\left(a-b\right)=60$$

$$=$$>  $$\left(a+b\right)\left(6\right)=60$$

$$=$$>  $$a+b=10$$ .........................(2)

Solving (1) and (2)

$$2a=16$$

$$=$$>  $$a=8$$

Substituting $$a=8$$ in equation(2)

$$=$$>  $$8+b=10$$

$$=$$>  $$b=2$$

$$\therefore\ $$Sum of their cubes $$=a^3+b^3=8^3+2^3=512+8=520$$

Hence, the correct answer is Option D