  We present an analysis of 39 nuclei and their early-type hosts in the Virgo
Cluster using ten broadband filters: F300W, F475W, F850LP, F160W, $u^*griz$,
and $K_s$. We describe the Virgo Redux program, which provides high-resolution
UV and NIR imaging. Combining this data with optical and NIR imaging from the
ACS Virgo Cluster Survey and the Next Generation Virgo Cluster Survey, we
estimate masses, metallicities and ages using simple stellar population (SSP)
models. For 19 nuclei, we compare to SSP parameters derived from Keck and
Gemini spectra and find reasonable agreement between the photometric and
spectroscopic metallicity: the RMS scatter is 0.3 dex. We reproduce the
nucleus-galaxy mass fraction of $0.33^{+0.09}_{-0.07}$ percent for galaxy
stellar masses $10^{8.4}-10^{10.3} M_\odot$ with a typical precision of
$\sim$35% for the nuclei masses. Based on available model predictions, there is
no single preferred formation scenario for nuclei, suggesting that nuclei are
formed stochastically through a mix of processes. Nuclei metallicities are
statistically identical to those of their hosts, appearing $0.07 \pm 0.3$ dex
more metal-rich on average -- although, omitting galaxies with unusual origins,
nuclei are $0.20\pm0.28$ dex more metal-rich. Nuclei appear to be $0.56 \pm
0.12$ dex more metal rich than ultra-compact dwarf galaxies (UCDs) at fixed
mass. We find no clear age difference between nuclei and their galaxies, with
nuclei displaying a broad range of ages. Interestingly, we find that the most
massive nuclei may be flatter and more closely aligned with the semi-major axes
of their hosts, suggesting that they formed through predominantly dissipative
processes.
