Capitalize if referring to a specific department or other academic unit by its full proper name. Office of Institutional Analysis, Division of Pediatric Surgery, Office of the President. But in general uses: president’s office. In cases of mulitple departments, lowercase all. Examples: Bob Hope, MD, is a professor of neurosurgery. But Bob Hope, MD, is a professor in the Department of Neurosurgery. In plural cases: Bob Hope, MD, is a professor in the departments of radiology, neurology and neurosurgery.
See institutes and centers.