  We combine archival HST and new JWST imaging data, covering the ultraviolet
to mid-infrared regime, to morphologically analyze the nuclear star cluster
(NSC) of NGC 628, a grand-design spiral galaxy. The cluster is located in a 200
pc x 400 pc cavity, lacking both dust and gas. We find roughly constant values
for the effective radius (r_eff ~ 5 pc) and ellipticity ({\epsilon} ~ 0.05),
while the S\'ersic index (n) and position angle (PA) drop from n ~ 3 to ~ 2 and
PA ~ 130{\deg} to 90{\deg}, respectively. In the mid-infrared, r_eff ~ 12pc,
{\epsilon} ~ 0.4, and n ~ 1-1.5, with the same PA ~ 90{\deg}. The NSC has a
stellar mass of log10 (M_nsc / M_Sun) = 7.06 +- 0.31, as derived through B-V,
confirmed when using multi-wavelength data, and in agreement with the
literature value. Fitting the spectral energy distribution, excluding the
mid-infrared data, yields a main stellar population's age of (8 +- 3) Gyr with
a metallicity of Z = 0.012 +- 0.006. There is no indication of any significant
star formation over the last few Gyr. Whether gas and dust were dynamically
kept out or evacuated from the central cavity remains unclear. The best-fit
suggests an excess of flux in the mid-infrared bands, with further indications
that the center of the mid-infrared structure is displaced with respect to the
optical center of the NSC. We discuss five potential scenarios, none of them
fully explaining both the observed photometry and structure.
