In recent articles by the present authors, the virial expansion formula was generalized to an assembly of quasiparticles, and the result was applied to a general discussion of the effect of the n-spin-wave interaction on the low-temperature spontaneous magnetization of the Heisenberg ferromagnet. The method, which may be called the method of quasiparticles, seems to give the simplest way of calculating the low-temperature expansion of the spontaneous magnetization. In this paper, (i) the Dyson T4 term for the Heisenberg ferromagnet is rederived by this method, and (ii) the corresponding expression for the Heisenberg ferromagnet with three exchange integrals Js, Jf, and Jb is derived, for cubic lattices. The result is used to calculate the T4 term in the spontaneous magnetization for the Heisenberg ferromagnet with first- and second-nearest-neighbor exchanges. This suggests a method of calculating the T5 and T6 terms in the expansion for these cases and the T4 term for the Heisenberg ferromagnet with a longer range exchange interaction.