Which Roman god was the god of music, poetry, and the sun? The answer is Apollo.
Apollo was a major god in both Greek and Roman religion, associated with music, poetry, light, healing, prophecy, archery, and—especially in later tradition—the sun. He was the son of Zeus and Leto and the twin brother of Artemis. In art, his most recognizable attribute is the lyre, reflecting his role as patron of singers, poets, musicians, and the Muses.
Apollo’s most famous sanctuary was at Delphi, where he presided over the Delphic Oracle. Worshippers consulted the oracle for guidance on personal, political, and religious questions. Apollo also had a complex relationship with disease: he could heal and protect people, yet myths such as the Iliad portray him as capable of sending plague with his arrows.
The sun association needs a little context. Apollo was originally distinct from Helios, the Greek personification of the sun. From about the 5th century BC onward, Apollo was increasingly identified with Helios, and Roman writers later connected him with Sol. That development explains why Apollo is a fair answer to the question, while Mercury, Bacchus, and Jupiter represent different divine roles.