Geometrical confinement can profoundly affect the dynamics of glass-forming polymers. In this context intense research has been mostly devoted to the understanding of how polymers subjected to 1-D confinement, that is, thin films, vitrify when cooled from the supercooled melt or recover equilibrium while in the glassy state. With the aim of extending our knowledge to other kinds of confinement, here we consider polystyrene (PS) nanospheres, that is, systems subjected to 3-D confinement. We investigate the physical aging following the enthalpy recovery in the glassy state employing fast scanning calorimetry, allowing heating/cooling rates as large as similar to 1000 K/s. These systems have been previously shown to exhibit suppressed glass transition temperature in comparison to bulk PS. We find accelerated recovery toward equilibrium, in line with previous findings on other confined polymer glasses exhibiting weak interactions with the substrate. Furthermore, the time evolution of the enthalpy exhibits two mechanisms of equilibration. Apart from a slow one, normally observed in proximity of the glass transition, a fast, mildly activated mechanism of equilibration is observed. We emphasize the analogy with bulk glasses, also exhibiting this behavior though on considerably larger time scales.