Multiple summation of a function of n variables

[as389 (Artem Strashko)]

Hello! Please, could you help me to calculate such a sum

Sum[F[x_1,x_2,...,x_n],{x_1,0,i},{x_2,0,i},...,{x_n,0,i}] 

for any positive and integer n? Also, in order to do this I need to build this function, because it is actually something like that

F[f[Sum[x_i,{i,1,n}]],x_1,x_2,a,b,c]. 

Is it right to write it in this form

F[f[Sum[x_i,{i,1,n}]]]

[as389 (Artem Strashko)]

To be specific, I need to calculate only the coefficient of 1/N in this sum