Clojure, 58 bytes
(fn[s](-(Math/pow(reduce + s)2)(reduce +(map #(* % %)s))))
Edit: I misunderstood the question
Clojure, 55 bytes
#(-(Math/pow(* %(+ % 1)1/2)2)(*(+ % 1)%(+(* 2 %)1)1/6))
Clojure, 58 bytes
(fn[s](-(Math/pow(reduce + s)2)(reduce +(map #(* % %)s))))
#(-(Math/pow(* %(+ % 1)1/2)2)(*(+ % 1)%(+(* 2 %)1)1/6))