Simplify the following expression.

$\frac{(62×62×62)-3(62×62×22)+3(62×22×22)-(22×22×22)}{8×8×8}$

125

$\frac{(62×62×62)-3(62×62×22)+3(62×22×22)-(22×22×22)}{8×8×8}$

(a - b)³ = a³ - b³ - 3ab(a-b)

Here a = 62 and b = 22

So,

$\frac{(62×62×62)-3(62×62×22)+3(62×22×22)-(22×22×22)}{8×8×8}$ = \(\frac{(62-22)^3}{512}\)

= \(\frac{64000}{512}\) = 125