Solve:
$8 l^{3} - 36 l^{2} m + 54 l m^{2} - 27 m^{3}$

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Solution

The given expression $8 l^{3} - 36 l^{2} m + 54 l m^{2} - 27 m^{3}$ can be solved as shown below:

$8 l^{3} - 36 l^{2} m + 54 l m^{2} - 27 m^{3} = (2 l)^{3} - (3 \times 2 l^{2} \times 3 m) + (3 \times 2 l \times 3 m^{2}) - (3 m)^{3} = (2 l - 3 m)^{3} (∵ (a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3})$

Hence, $8 l^{3} - 36 l^{2} m + 54 l m^{2} - 27 m^{3} = (2 l - 3 m)^{3}$ .

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