Without actually calculating the cubes, find the value of the following:
$(- 15)^{3} + (28)^{3} + (- 13)^{3}$

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Solution

$(- 15)^{3} + (28)^{3} + (- 13)^{3}$
We know that $a^{3} + b^{3} + c^{3} = 3 a b c,$ if $a + b + c = 0$
Here $a + b + c = - 15 + 28 + (- 13) = 0$
$(- 15)^{3} + (28)^{3} + (- 13)^{3}$
$= 3 \times (- 15) \times 28 \times (- 13)$
$= 16380$

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