  A generalization of the volume conjecture relates the asymptotic behavior of
the colored Jones polynomial of a knot to the Chern--Simons invariant and the
Reidemeister torsion of the knot complement associated with a representation of
the fundamental group to the special linear group of degree two over complex
numbers. If the knot is hyperbolic, the representation can be regarded as a
deformation of the holonomy representation that determines the complete
hyperbolic structure. In this article we study a similar phenomenon when the
knot is a twice-iterated torus knot. In this case, the asymptotic expansion of
the colored Jones polynomial splits into sums and each summand is related to
the Chern--Simons invariant and the Reidemeister torsion associated with a
representation.
