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Symbolic Sum or Sum???


Actually I have a problem for solving a double sum whose limits are
running from ( - Infinity ) to ( + Infinity ). I attempted this sum
in several ways without a satisfactory result:

1-Attempt) :     
===========
            

Needs["Algebra`SymbolicSum`"]
BeginPackage["Algebra`","SymbolicSum`"]

F[x0_,y0_, N_, M_,n_,m_]:= 1/((x0 + n N)^2 + (y0 + m M)^2)^(3/2)



SymbolicSum[F[x0,y0,N,M,n,m] , {m,Infinity}, {n,Infinity} ]

                              



NSum[ F[1,0,3,3,n,m] , {m,-infinity,Infinity}, 
                               {n,-Infinity,Infinity} ]


S[k_]:= NSum[ F[1,0,3,3,n,m] , {m,-k,k}, {n,-k,k} ]
Table[S[i],{i,0,Infinity}]


None of this this forma could bring me further in the solution of
F[...].


I thank you in advance for any help you can provide me.



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