Nuclear rings in barred galaxies are sites of active star formation (SF). We investigate SF and its feedback effects occurring in barred galaxies, for the first time, using high-resolution grid-based hydrodynamic simulations. The gaseous medium is assumed to be infinitesimally thin, isothermal, and unmagnetized. The SF recipes include a density threshold corresponding to the Jeans condition, a SF efficiency of 1%, and momentum feedback via Type II supernova events together with stellar-wind mass loss. To investigate various environments, we vary the gas sound speed as well as the efficiency of momentum injection in the in-plane direction. We find that when the sound speed is small, the surface density of a ring becomes largely independent of the azimuthal angle, resulting in star-forming regions distributed over the whole length of the ring. When the sound speed is large, on the other hand, the ring achieves the largest density at the contact points between the dust lanes and the ring where SF occurs preferentially, leading to a clear age gradient of star clusters in the azimuthal direction. Since rings shrink with time, a radial age gradient of star clusters naturally develop regardless of sound speed, consistent with observations. SF persists over 200 Myr, with an average rate of ${sim}1.3M_{odot}/yr$ similar to observed values. Rings gradually become hostile to SF as they lose gas into stars and turbulent motions dominate.