Use the distributive property (of which the FOIL method is a special case):
(a - b) (a² + ab + b²)
= (a - b) a² + (a - b) ab + (a - b) b²
= (a³ - a²b) + (a²b - ab²) + (ab² - b³)
= a³ - b³
Alternatively, you can distribute the quadratic expression over each term in a - b :
(a - b) (a² + ab + b²)
= a (a² + ab + b²) - b (a² + ab + b²)
= (a³ + a²b + ab²) - (a²b + ab² + b³)
= a³ - b³
