If a - 2b + 3c = 0; state the value of a³ - 8b³ + 27c³.

If x + 5y = 10; find the value of x³ + 125y³ + 150xy - 1000.

If a + b = 11 and a² + b² = 65; find a³ + b³.

If x, y and z are three different numbers, then prove that :

x² + y² + z² - xy - yz - zx is always positive.