KöMaL 2009 B4169

Prove that if $a$, $b$, $c$ are pairwise distinct positive integers then $S$=(42$a$+43$b$+43$c$)$^3$+(43$a$+42$b$+43$c$)$^3$+(43$a$+43$b$+42$c$)$^3$ -3(42$a$+43$b$+43$c$)(43$a$+42$b$+43$c$)(43$a$+43$b$+42$c$) is divisible by 128 but is not a perfect power of 2.