Quantum well (QW) resonances in Fe(001)/MgO/Fe/MgO/Fe double barrier magnetic tunnel junctions are calculated from first principles. By including the Coulomb blockade energy due to the finite size islands of the middle Fe film, we confirm that the oscillatory differential resistance observed in a recent experiment [T. Nozaki, Phys. Rev. Lett. 96, 027208 (2006)10.1103/PhysRevLett.96.027208] originates from the QW resonances from the Delta1 band of the Fe majority-spin channel. The primary source of smearing at low temperatures is shown to be the variation of the Coulomb blockade energy.