  In this paper, we first establish explicit evaluations of six classes of
hyperbolic sums by special values of the Gamma function by using the tools of
the Fourier series expansions and the Maclaurin series expansions of a few
Jacobi elliptic functions developed in our previous paper. Then, using the
method of contour integrations involving hyperbolic and trigonometric
functions, we establish explicit evaluations of two families of Berndt-type
integrals of order three by special values of the Gamma function. Furthermore,
we present some interesting consequences and illustrative examples.
