(x - y)^{3} - (27 - y)^{3}

${\left(x-y\right)}^{3}-{\left(27-y\right)}^{3}$
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Use the difference of two cubes:
${a}^{3}-{b}^{3}=\left(a-b\right)\left({a}^{2}+ab+{b}^{2}\right)$
Substitute a=x−y and b=27−y:
$=\left[\left(x-y\right)-\left(27-y\right)\right]\left[\left(x-y{\right)}^{2}+\left(x-y\right)\left(27-y\right)+\left(27-y{\right)}^{2}\right]\phantom{\rule{0ex}{0ex}}=\left[x-y-27+y\right]\left[\left({x}^{2}-2xy+{y}^{2}\right)+,\left(27x-27y-xy+{y}^{,}2\right)+\left(729-54y+{y}^{2}\right)\right]\phantom{\rule{0ex}{0ex}}=\left(x-27\right)\left({x}^{2}-3xy+3{y}^{2}+27x-81y+729\right)$