The verb “bring up" along with its noun form “upbringing" are generally used for the moral and social training of growing children. This is mostly associated with the training the children receive from their parents, teachers, governesses or other seniors at home or at the locality.
On the other hand, the verb “educate" and its noun form “education" are related to the intellectual, literary or cultural training people get at institutes like schools, colleges and universities.
Thus, a “well brought up" person is one with good human qualities, and a “badly brought up" child is rough and selfish. On the other hand, a “well educated person" is one who has gone through proper schooling.
Ram's parents died in his infancy, but his grandparents brought him up well, and he later became a well mannered person.
Ram could not afford the city college and was educated in the local one.