We study the spatially resolved stellar populations of 444 galaxies at 0.3 < z < 6.0 in two clusters (WHL 0137-08 and MACS 0647+70) and a blank field, combining imaging data from the Hubble Space Telescope and JWST to perform spatially resolved spectral energy distribution (SED) modeling using piXedfit. The high spatial resolution of the imaging data combined with magnification from gravitational lensing in the cluster fields allows us to resolve a large fraction of our galaxies (109) to subkiloparsec scales. At redshifts around cosmic noon and higher (2.5 less than or similar to z less than or similar to 6.0), we find mass-doubling times to be independent of radius, inferred from flat specific star formation rate (sSFR) radial profiles and similarities between the half-mass and half-SFR radii. At lower redshifts (1.5 less than or similar to z less than or similar to 2.5), a significant fraction of our star-forming galaxies shows evidence for nuclear starbursts, inferred from a centrally elevated sSFR and a much smaller half-SFR radius compared to the half-mass radius. At later epochs, we find more galaxies suppress star formation in their centers but are still actively forming stars in the disk. Overall, these trends point toward a picture of inside-out galaxy growth consistent with theoretical models and simulations. We also observe a tight relationship between the central mass surface density and global stellar mass with similar to 0.38 dex scatter. Our analysis demonstrates the potential of spatially resolved SED analysis with JWST data. Future analysis with larger samples will be able to further explore the assembly of galaxy mass and the growth of their structures.