  Lattice sums of cuboidal lattices, which connect the face-centered with the
mean-centered and the body-centered cubic lattices through parameter dependent
lattice vectors, are evaluated by decomposing them into two separate lattice
sums related to a scaled cubic lattice and a scaled Madelung constant. Using
theta functions we were able to derive fast converging series in terms of
Bessel functions. Analytical continuations of these lattice sums are discussed
in detail.
