Generally speaking, No, termites do not eat concrete. Termites cannot derive any nutrition from concrete so the only reason they may attempt to tunnel their way through it is in order to get through the concrete to lumber that may lay behind it.
Most concrete is hard enough that termites cannot chew through it. However, older degraded concrete is occasionally weak enough for termites to make their way through. The same has been known to be true with lime mortar which is common with brickwork. Termites have been known to make their way through the lime mortar between brickwork to get to the wood behind them.
Typically termites will not attempt to burrow their way through concrete without first finding a hole large enough for them to fit through. This does not really have to be very big. A hole just a bit larger than the termites head is enough for them to enter and begin tunneling, however, they prefer holes twice this size to allow for two-way traffic: in and out. Still termites are tiny so a hole the width of two termite heads is not very big and easy for termites to work their way through if the concrete or mortar mix is weakened enough for their jaws to chew into.