Question

Without actually calculating the cubes . Evaluate 14³+13³-27³

Answer 1

use the formula a3 +b3 -c3

Answer 2

If 14+13-27=0
or, 14-14=0
Then Using using formula if,
a+b+c=0 then
$a {}^{3} + b {}^{3} + c {}^{3} = 3abc$
$so \: a {}^{3} + b {}^{3} + c {}^{3} = 3abc \\ = 3 \times 14 \times 13 \times (- 27) \\ a {}^{3} + b {}^{3} + c {}^{3} = - 14742$