The difference between the cubes of two given natural numbers is 6272 , while the positive difference between the two given numbers is 8. What is the sum of the cubes of the two given numbers?

If 2x + 3y = 16 and xy = 9, then find 8x³ + 27y³

If x + y = 25 and xy = 20, then find the value of x³ + y³.

If $(x + {1\over x}) = \sqrt6 $, and x > 1, what is the value of $(x^8 - {1 \over x^8}) $?