  We consider the double twist link $J(2m+1, 2n+1)$ which is the two-bridge
link corresponding to the continued fraction $(2m+1)-1/(2n+1)$. It is known
that $J(2m+1, 2n+1)$ has reducible nonabelian $SL_2(\mathbb{C})$-character
variety if and only if $m=n$. In this paper we give a formula for the volume of
hyperbolic cone-manifolds of $J(2m+1,2m+1)$. We also give a formula for the
A-polynomial 2-tuple corresponding to the canonical component of the character
variety of $J(2m+1,2m+1)$.
