Flying capacitor voltage balancing is critical for the performance of flying capacitor multilevel (FCML) converters. This paper investigates the fundamentals of intrinsic capacitor voltage balancing of multiphase FCML converters with coupled inductors. It is shown that the coupled inductor provides a new, intrinsic mechanism of flying capacitor voltage balancing that is robust to periodic disturbances and independent of the inductor quality factor. This balancing mechanism is typically stronger than natural balancing. The imbalances with uncoupled inductors are analytically predicted and shown to be dependent on the quality factor of the inductor, thus leading to much larger imbalances compared to the coupled inductor balancing mechanism. A dynamic model for voltage balancing of the flying capacitors with coupled inductors is derived and used to estimate the time required to settle from an initial imbalance. The theoretical analysis is verified with simulations and experimental results. Adding coupled inductors to FCML converters can greatly enhance the robustness of FCML converters against physical nonidealities and periodic disturbances.