  Let $C(2n, 3)$ be the family of two bridge knots of slope $(4n+1)/(6n+1)$. We
calculate the volumes of the $C(2n, 3)$ cone-manifolds using the Schl\"{a}fli
formula. We present the concrete and explicit formula of them. We apply the
general instructions of Hilden, Lozano, and Montesinos-Amilibia and extend the
Ham, Mednykh, and Petrov's methods. As an application, we give the volumes of
the cyclic coverings over those knots. For the fundamental group of $C( 2n,
3)$, we take and tailor Hoste and Shanahan's. As a byproduct, we give an
affirmative answer for their question whether their presentation is actually
derived from Schubert's canonical 2-bridge diagram or not.
