The three-dimensional repulsive Hubbard model is investigated using the strong-coupling diagram technique. For half-filling, the boundary between paramagnetic and antiferromagnetic states is determined for the range of the Hubbard repulsion 4t≤ U≤12t, where t is the hopping integral between neighboring sites. Along this boundary, the density of states is calculated, and it demonstrates the Mott transition at U≈9t. For U≥6t and half-filling, the density of states has the shape inherent in the strong electron repulsion, while for U=4t, its shape points to weak coupling. The dependence of the Néel temperature T_(rm N) on the electron concentration n̄ is investigated for the cases U=4t and 12t. In the former case, T_(rm N) decreases monotonously with n̄, while in the latter case, there is a plateau in the dependence near n̄=0.87. The plateau is connected to a reconstruction of the density of states caused by an effective weakening of electron coupling due to electron depopulation. For U=12t and half-filling, the magnetic critical exponent γ≈1.4, which is close to the value in the Heisenberg model. Some features resembling the first-order phase transition, revealing themselves in a finite crystal, are discussed.