We consider the paraxial model for a nonlinear resonator with a saturable absorber beyond the mean-field limit and develop a method to study the modulational instabilities leading to pattern formation in all three spatial dimensions. For achievable parametric domains we observe total radiation confinement and the formation of 3D localised bright structures. At difference from freely propagating light bullets, here the self-organization proceeds from the resonator feedback, combined with diffraction and nonlinearity. Such cavity light bullets can be independently excited and erased by appropriate pulses, and once created, they endlessly travel the cavity roundtrip. Also, the pulses can shift in the transverse direction, following external field gradients.
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