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 product of the two given numbers?

Expand and simplify the algebraic expression:

(x - 5)² + (x + 3)² + 4x

If (a³ + b³ + c³ - 3abc) = 405, and (a - b)² + (b - c)² + (c -a)² = 54, find the value of (a + b + c).

If (a + b + c) = 13, and (ab + bc + ca) = 54, find the value of (a² + b² + c²).