Due to the work of Thurston, a cusped manifold, such as a hyperbolic knot complement in the 3-sphere, can be well understood as we decompose it into ideal tetrahedra. In particular, Zickert showed that the volume and Chern-Simons invariant of a cusped manifold can be computed in terms of ideal tetrahedra. In this thesis, we generalize the formula of Zickert to a Dehn-filled manifold. Also, we apply our formula to an octahedral decomposition of a link complement which results in a diagrammatic formula for computing the volume and Chern-Simons invariant.