Lúthien clearly had a magical power accessible via her singing:
In Lay of Leithian Canto XIII, Lúthien manages to sing Morgoth (and all the fires around) to sleep.
Later, Lúthien swayed Mandos with her song:
Their spirits were gathered in the Halls of Mandos in the Uttermost West, and there Lúthien sang a song of such extraordinary power and beauty that it moved even the implacable heart of Mandos himself. So she was granted a unique fate, to become mortal and return to Middle-earth with Beren, where they dwelt for a time in happiness on the green island of Tol Galen in the River Adurant.
Did Tolkien explicitly indicate the connection between in-universe power of Song as exibited by Lúthien; and Ainulindalë's explanation that the whole of the universe was sung into existence via The Music of the Ainur under Eru's direction?