A heterometallic hexanuclear mixed-valence Co-Dy cluster [Co₄Dy₂(OH)₂(O₂CCMe₃)₈(HO₂CCMe₃)₂(teaH)₂(N₃)₂]·2(EtOH) (1) has been prepared from the reaction of dinuclear Co(II) pivalate with triethanolamine and azide ligands and characterized by elemental analysis, IR spectroscopy, and X-ray crystallography. The metal atoms in the {Co^II₂Co^III₂Dy^III₂} cluster core are bridged by two μ₃-hydroxy groups, two azide N₃^- anions, six pivalate residues, and two doubly deprotonated teaH^2- ligands. A theoretical model has been developed to explain the magnetic behavior of 1. The model takes into account the crystal fields acting on the Dy^III ions and the anti- and ferromagnetic exchange interactions in the pairs Co-Dy and Co-Co, respectively. The Stark structure for the Dy^III ions is calculated with due account of the covalence effects within the frames of the exchange charge model of the crystal field. It is demonstrated that at low temperatures the magnetic properties of the cluster are determined by the interaction of the ground state Kramers doublet of the Co^II ion with those Stark levels of the Dy^III ions, for which the energies are smaller than the spin-orbital coupling parameter. At higher temperatures, the population of the Co^II ion multiplets with the angular momentum values 3/2 and 5/2 leads to the increase of the magnetic susceptibility. The observed temperature dependence of the χ_MT product and field dependence of the magnetization are satisfactorily explained within the framework of the suggested model.