  Using the three-particle quantization condition recently obtained in the
particle-dimer framework, the finite-volume energy shift of the two lowest
three-particle scattering states is derived up to and including order $L^{-6}$.
Furthermore, assuming that a stable dimer exists in the infinite volume, the
shift for the lowest particle-dimer scattering state is obtained up to and
including order $L^{-3}$. The result for the lowest three-particle state agrees
with the results from the literature, and the result for the lowest
particle-dimer state reproduces the one obtained by using the Luescher
equation.
