05AB1E, 1111 7 bytes
05AB1E uses CP-1252 encoding.
ÐPŠO;sO¹·-P8*¹/P Explanation
O # implicitsum input [a,b,c] Ð ¹ # triplicatepush input P # product of one copy Š # move to bottom of stack O # sum the second copyagain ; · # halvemultiply theby sum2 s- # subtract the third copy from this P # productsum ¹/ 8* # multiplydivide by 8input P / # divide the product by this