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$latex (a-b)^3=a^3-3a^2b+3ab^2-b^3$

So,

$latex

begin{array}{rcl}

a^3-b^3&=&(a-b)^3+3a^2b-3ab^2

&=&(a-b)(a-b)^2+3a^2b-3ab^2

&=&(a-b)(a^2-2ab+b^2)+(a-b)(3ab)

&=&(a-b)(a^2+ab+b^2)

end{array}

$

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