The energy spectrum of an electron in a cylindrical wire with an infinitely high barrier at the boundary and with a parabolic potential inside the wire is obtained. The transformation of the spectrum with increasing oscillator (Ω) and magnetic (ω_H) frequencies is investigated. The polaron corrections arising in the electronic energy levels and the translational effective mass as a result of the interaction with bulk and interface modes are obtained by the perturbation-theory method in the Wigner-Brillouin approximation, and their dependences on the magnetic field are determined. The magnetic polaron resonance is studied and the splitting of the resonance polaron levels is calculated.