The nuclei don't have a permanent electric dipole because they have a positive homogeneous distributed net charge. The requirement for the existence of a permanent electric dipole is that the body has positive and negative charges distributed in an inhomogeneous way, where positive and negative charges are well-differentiated and incapable of mooving its relative position. This is exactly what happens with molecules.
Magnetic dipole moments are related to sub particle movement inside atomic particles. That's why nuclei and molecules have it.
