how should I cal. the sum of all the combinations?

Dear All, For one vector A=(a1, a2, ...a3000). I want to calculate the sum(ai * aj^2) where i,j are different indices, i not equal to j. If I use the co_vol function it costs too much time to run the code. So I am thinking, is there a formula exisiting to calculate this sum? Like the case I showed under the "%%%%%%%%" line below, for the sum(ai * aj* ak) case. (where i j k are different from each other)

Thanks a lot in advance

function co_vol=co_vol(in)

in=in; N=length(in);

% aa=zeros(N^2,1); aae=[];

parfor i=1:N for j=1:N if j~=i ae=in(i)*in(j)^2; else ae=0; end

      aae =[aae ae];
  end
end

co_vol=sum(aae); end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 I am calculating the sum(ai * aj * ak) where i,j,k are different indices. based on this formula: (sum(A)^3-3*sum(A.^2)*sum(A)+2*sum(A.^3))

instead of the code below. This saves me a lot of computation time. function co_cov=co_cov(in)

in=in; N=length(in);

aae=[];

 parfor i=1:N
  for j=1:N
      for k=1:N
      if (i~=j)&&(i~=k)&&(j~=k)
    ae=in(i)*in(j)*in(k);
      else
          ae=0;
      end
 aae=[aae ae];

      end

end

end

co_cov=sum(aae ); end