We have investigated the radial g-r color gradients of early-type galaxies in the Sloan Digital Sky Survey (SDSS) DR6 in the redshift range 0.00<z<0.06. The majority of massive early-type galaxies show a negative color gradient (red-cored) as generally expected for early-type galaxies. On the other hand, roughly 30% of the galaxies in this sample show a positive color gradient (blue-cored). These "blue-cored" galaxies often show strong $H{eta}$ absorption-line strengths and/or emission-line ratios that are indicative of the presence of young stellar populations. This implies that most of the residual star formation in early-type galaxies is centrally concentrated. Blue-cored galaxies are predominantly low-velocity dispersion systems. A simple model shows that the observed positive color gradients are visible only for a billion years after a star formation episode for the typical strength of recent star formation. The observed effective radius decreases and the mean surface brightness increases due to this centrally concentrated star formation episode. As a result, the majority of blue-cored galaxies may lie on different regions in the fundamental plane (FP) from red-cored ellipticals. However, the position of the blue-cored galaxies on the FP cannot be solely attributed to recent star formation but requires substantially lower velocity dispersion. We conclude that a low-level of residual star formation persists at the centers of most of low-mass early-type galaxies, whereas massive ones are mostly quiescent systems with metallicity-driven red cores.