VTMO 2015 — Grade 7 — final Question 2

$S \left[A\right]$ sums the element sums of all subsets, including the empty subset. Find $S \left[\{ 1 , 2 , 3 \}\right]$, and prove $S \left[\{ a , b , c , d \}\right]$ divisible by $8$ for distinct natural elements.