We present an analysis of the optical colors of 413 Virgo cluster early-type dwarf galaxies (dEs), based on Sloan Digital Sky Survey imaging data. Our study comprises (1) a comparison of the color-magnitude relation (CMR) of the different dE subclasses that we identified in Paper III of this series, (2) a comparison of the shape of the CMR in low and high-density regions, (3) an analysis of the scatter of the CMR, and (4) an interpretation of the observed colors with ages and metallicities from population synthesis models. We find that the CMRs of nucleated (dE(N)) and non-nucleated dEs (dE(nN)) are significantly different from each other, with similar colors at fainter magnitudes (r > 17 mag), but increasingly redder colors of the dE(N)s at brighter magnitudes. We interpret this with older ages and/or higher metallicities of the brighter dE(N)s. The dEs with disk features have similar colors as the dE(N)s and seem to be only slightly younger and/or less metal-rich on average. Furthermore, we find a small but significant dependence of the CMR on local projected galaxy number density, consistently seen in all of u-r, g-r, and g-i, and weakly i-z. We deduce that a significant intrinsic color scatter of the CMR is present, even when allowing for a distance spread of our galaxies. No increase of the CMR scatter at fainter magnitudes is observed down to r = 17 mag (Mr = -14 mag). The color residuals, i.e., the offsets of the data points from the linear fit to the CMR, are clearly correlated with each other in all colors for the dE(N)s and for the full dE sample. We conclude that there must be at least two different formation channels for early-type dwarfs in order to explain the heterogeneity of this class of galaxy. (Abridged)
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