How can I persuade Maple 16 to simplify such double sums to zero?  (The competition does it in a snap).

sum(sum( m[i]*m[j]*(x[i] - x[j]), i=1..N), j=1..N);

sum(sum( m[i]*m[j]*(x[i] - x[j])*(y[i] - y[j])*(z[i] - z[j]), i=1..N), j=1..N);

The sum elements are antisymmetric in the (i,j) indices so for every element there is another one cancelling it.