  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.
