What is the cure of fibroadenomas?

Its benign. Commonly found in breast, fibroadenomas are benign tumors. So they can be left along if small and asymptomatic. Some of them can grow slowly, in that case surgical removal may be advised. You should be under supervision of a good breast specialist who can examine and guide you in the future.
Genetics. We have not identified a behavior or external cause for these. They often show up in the 3rd decade of life (20s). They don't often regress spontaneously, but if you have it removed surgically you should expect cure.