Here is the complete formula of A3 + B3:
a³ + b³ = (a + b)(a² – ab + b²)
you know that
(a + b)³ = a³ + 3ab(a + b) + b³
then a³ + b³ = (a + b)³ – 3ab(a + b)
= (a + b)[(a + b)² – 3ab]
= (a + b)(a² + 2ab + b² – 3ab)
= (a + b)(a² – ab + b² )
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