  In this paper, we develop highly accurate Nystr\"{o}m methods for the volume
integral equation (VIE) of the Maxwell equation for 3-D scatters. The method is
based on a formulation of the VIE equation where the Cauchy principal value of
the dyadic Green's function can be computed accurately for a finite size
exclusion volume with some explicit corrective integrals of removable
singularities. Then, an effective interpolated quadrature formula for tensor
product Gauss quadrature nodes in a cube is proposed to handle the
hyper-singularity of integrals of the dyadic Green's function. The proposed
high order Nystr\"{o}m VIE method is shown to have high accuracy and
demonstrates $p$-convergence for computing the electromagnetic scattering of
cubes in $R^3$.
