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This work is devoted to the analysis of the complex nonlinear mechanism of three-dimensional (3D) energy channeling emerging in a locally resonant unit-cell model. The system under consideration comprises of an external mass subjected to a 3D nonlinear local potential with an internal spherical rotator (ref. Fig. 1). In the present study we focus on the analysis of the regimes of 3D bi-directional (ref. Fig. 2) and uni-directional energy (ref. Fig. 3) transport realized in the limit of low energy excitation. The considered system exhibits rich nonlinear dynamical phenomena and bifurcation of highly non-stationary regimes. In the considered low energy limit, we explore analytically the two distinct families of non-stationary regimes corresponding to the in-plane as well as the out-of-plane energy channeling. The phenomenon of bi-directional energy channeling observed in conservative systems is manifested in the form of 3D recurrent transformation (ref. Fig. 2) of general in-plane oscillations of the external element to its orthogonally reoriented in-plane and out-of-plane oscillations. In contrast, the uni-directional energy channeling is manifested in the form of irreversible (uni-directional, ref. Fig. 3) energy transport across mutually orthogonal directions and is observable in non-conservative systems with dissipative mechanisms like viscous damping. Both these mechanisms are fully controlled by the internal spherical rotator coupled to the external mass. To this end we invoke regular multi-scale analysis that enables to characterize and predict the intrinsic mechanisms governing the highly non-stationary regimes of the three-dimensional energy flow resulting in a reduced slow flow model (response corresponding to red curves in Fig. 2, 3). Numerical simulations are found to be in extremely good correspondence with the analytical results.