If a + b + 2c = 0, prove that a³ + b³ + 8c³ = 6abc

If x + 2y - 3 = 0, then find the value of x³ + 8y³ + 6x²y + 12xy² - 125.

If x + y = 4, find the value of x³ + y³ + 12xy - 64

Without actually calculating the cubes, find the values of:

(i) (27)³ + (-17)³ + (-10)³

(ii) (-28)³ + (15)³ + (13)³