A consideration of various ideas set forth within the scaled particle theory of hard particle fluids, which are also applicable to systems whose particles interact via attractive potentials, suggests that cavity formation plays an important role in the molecular mechanism of the liquid-to-vapor transition. Umbrella sampling Monte Carlo simulations are used to calculate the reversible work of forming cavities of various sizes within the superheated Lennard-Jones liquid maintained at several negative pressures. A critical cavity size is found to occur, beyond which the liquid would phase separate if not for a density constraint that is applied during the simulation. The work of forming this critically sized cavity and its radius is found to decrease as the liquid approaches the spinodal. A critical cavity size is also found for the superheated liquid at positive pressures. The focus on cavity growth in superheated liquids amounts to a new way of studying bubble nucleation and should lead to an improved molecular-based understanding of the kinetics of first-order phase transitions in liquids.