  (Abridged) We present a comprehensive analysis of the spatially resolved
stellar population properties of 26 early-type dwarf (dE) galaxies in the Virgo
cluster. Using Lick/IDS absorption line indices we derive simple stellar
population(SSP)-equivalent age, metallicity and [$\alpha$/Fe] abundance ratio.
In particular, we focus on the comparison of the stellar populations between
the central nucleus and the surrounding galactic main body. The stellar
populations of the nuclei are, for most dEs, significantly younger than those
of the respective galactic main bodies, with an average difference of 3.5 Gyr.
We find only five dEs with significantly older nuclei than their galactic main
bodies. Furthermore, we observe most dE nuclei to be more metal rich compared
to their host galaxies. These age and metallicity behaviours are shown by
almost all dEs brighter than M$_{\it r}$ = -17 mag.
  We also examine the presence of radial gradients in the SSP parameters for a
subset of 13 dEs (up to 1.2 kpc or 15 arcsec radius). We notice two different
types of gradients, namely smooth profiles that include the nucleus, and
profiles where a break occurs between the nucleus and the rest of the galaxy.
Nevertheless, an overall trend of increasing age and decreasing metallicity
with radius exists, consistent with earlier studies.
