Question

a cube + b cube =?
a + b the whole cube =?
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Answer 1

$(a+b)^3=a^3+b^3+3ab(a+b)$
or $(a+b)^3=a^3+b^3+3a^2b+3ab^2$
$(a-b)^3=a^3-b^3-3ab(a-b)$
or $(a-b)^3=a^3-b^3-3a^2b+3ab^2$
$a^3 + b^3= (a+b)(a^2+b^2-ab)$
$a^3 - b^3 = (a-b)(a^2+b^2+ab)$
Note: Last two identities can be derived from first two.