Self-assembly of cylinder-forming diblock copolymers under spherical confinement is studied using real-space self-consistent field theory calculations (SCFT). Various microstructures are found at different confinement dimensions and surface fields. Most of these microstructures are center-symmetric and they could not be formed in bulk or under planar and cylindrical confinements. It is also observed that the interactions between the confinement surface and the polymers have a large effect on the self-assembly. When the spherical confinement's surface attracts the short blocks, the self-assembled structures become similar to those under a neutral surface field. On the other hand, when the spherical confinement's surface attracts the long blocks, the equilibrium structures become different from those under a neutral surface field.