The sum of the cubes of two given natural numbers is 9728, while the sum of the two given numbers is 32. What is the positive difference between the cubes of the two given numbers?

If (x + $\frac{1}{x}$) = 6, and x > 1, find the value of (x² - $\frac{1}{x^2}$).

If x² - $\frac{1}{x^2}$ = 4 $\sqrt2$, what is the value of x⁴ - $\frac{1}{x^4}$?

Simplify the given expression.

$\frac{[120\times120\times120-100\times100\times100]}{[120\times120+120\times100+100\times100]}$