Cultured (kltrd), a.
1. Under culture; cultivated. "Cultured vales." Shenstone.
2. Characterized by mental and moral training; disciplined; refined; well-educated. The sense of beauty in nature, even among cultured people, is less often met with than other mental endowments. I. Taylor. The cunning hand and cultured brain. Whittier.
Shades of meaning
Fernald has no entry of its own for cultured; he lists it under polite.
Where he writes about it:
Polished refers to external elegancies of speech and manner without reference to spirit or purpose; as, a polished gentleman or a polished scoundrel; cultured refers to a real and high development of mind and soul, of which the external manifestation is the smallest part. — from polite