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We calculate the Chern-Simons invariants of the hyperbolic orbifolds of theknot with Conway's notation $C(2n, 3)$ using the Schl\"{a}fli formula for thegeneralized Chern-Simons function on the family of $C(2n,3)$ cone-manifoldstructures. We present the concrete and explicit formula of them. We apply thegeneral instructions of Hilden, Lozano, and Montesinos-Amilibia and extend theHam and Lee's methods. As an application, we calculate the Chern-Simonsinvariants of cyclic coverings of the hyperbolic $C(2n,3)$ orbifolds.

Explicit formulae for Chern-Simons invariants of the hyperbolic orbifolds of the knot with Conway's notation $C(2n, 3)$