The properties of surface plasmon modes and switching gaps for extraordinary mode in the 3-D magnetized plasma photonic crystals (MPPCs) with body-centered-cubic lattices, that are composed of the core tellurium (Te) spheres with surrounded by the magnetized plasma shells inserted in the air, are theoretically investigated in detail by the plane wave expansion method, as the magneto-optical Voigt effects of magnetized plasma are considered (the incidence electromagnetic wave vector is perpendicular to the external magnetic field at any time). Our computing results show that the complete photonic bandgaps for extraordinary mode and two flatbands regions can be observed. The optical switching can be realized by such MPPCs, which can be tuned by the radius of core Te sphere, the plasma density and the external magnetic field, respectively. The flatbands regions are determined by the existence of surface plasmon modes. The numerical simulations also demonstrate that the interesting properties of surface plasmon modes can be found. If the thickness of magnetized plasma shell is larger than a threshold value, the band structures for extraordinary mode will be similar to those obtained from the same structure containing the pure magnetized plasma spheres. In this condition, the inserted core sphere also has no effect on the band structures. It is worth to be noticed that the upper edge frequencies of two flatbands regions will not depend on the topology of lattice. However, to the different topologies of lattices, if the thickness of magnetized plasma shell is close to zero, the frequencies of lower edges will be convergence to two different constants.