$S$=$2$+$2^{2}$+$2^{3}$+$2^{4}$+$2^{5}$+$2^{6}$+$2^{7}$+$2^{8}$
$S$=($2$+$2^{2}$)+($2^{3}$+$2^{4}$)+($2^{5}$+$2^{6}$)+($2^{7}$+$2^{8}$)
$S$=$6$ + $2^{2}$($2$+$2^{2}$) + $2^{4}$($2$+$2^{2}$) + $2^{6}$($2$+$2^{2}$)
$S$=$6$ + $2^{2}$.$6$+ $2^{4}$.$6$ + $2^{6}$.$6$
$S$=$6$($1$ + $2^{2}$+ $2^{4}$ + $2^{6}$) $⋮$ $-6$
Vậy $S$ $⋮$ $-6$ ($đpcm$)