a³ - b³ = (a - b) (a² + ab + b²)
You can see why this works if you expand the right side as
a (a² + ab + b²) - b (a² + ab + b²)
(a³ + a²b + ab²) - (a²b + ab² + b³)
Both the a²b and ab² terms cancel, leaving you with a³ - b³.
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