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 .

The metallicity of both nuclei and galactic main bodies correlates with the total luminosity of the dEs .
However , the metallicity of the nuclei covers a larger range ( +0.18 to -1.22 dex ) than that of the galactic main bodies , which all have sub-solar metallicity .
The ages of dE nuclei show a statistically significant correlation with the local projected galaxy density within the cluster , such that younger ages are predominantly observed outside of the high-density central cluster region .
The alpha-element abundance ratios are consistent with solar for both nuclei and galactic main bodies .

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 .
The \alpha -abundance ratio as function of radius is consistent with no gradient .

Possible formation scenarios for the nuclei of dEs are discussed .
The young and metal-enhanced population of nuclei suggests that these might have formed at later epochs , or the termination of star formation activity in the nuclei might have occured relatively late , perhaps due to continuous infall of gas into the central potential well .
Our stellar population analysis suggests that the merging of globular clusters is not an appropriate scenario for the formation of most dE nuclei , at least not for the brighter dEs .
We speculate that there might be different formation processes which are responsible for the formation of dEs and their nuclei depending on their luminosity .