Oxidation of SiC produces SiO2 while CO is released. A ``reoxidation'' step at lower temperatures is, however, necessary to produce high-quality SiO2. This step is believed to cleanse the oxide of residual C without further oxidation of the SiC substrate. We report first-principles calculations that describe the nucleation and growth of O-deficient C clusters in SiO2 under oxidation conditions, fed by the production of CO at the advancing interface, and their gradual dissolution by the supply of O under reoxidation conditions. We predict that both CO and CO2 are released during both steps.