As indicated at the links Mofi kindly provided, the 310A's filament operates at 10 volts, while the 6C6's filament operates at 6.3 volts. That in itself rules out direct substitution. There are other electrical differences as well, including maximum rated plate dissipation of the 310A being almost 3 times higher than for the 6C6, as well as significant differences in transconductance and other parameters.
Regards,
-- Al
Regards,
-- Al