Interpretation 1: The Song of Songs is a song of (or by) Solomon.
Arguments in favour of this view:
1. The short Hebrew word “le” as used in the header generally means of, as it does in the psalms of David, of Asaph, or of the sons of Korah.
2. In view of the Hebrew word “le,” Psalm 72:1–20, often read as a psalm about Solomon, should be a psalm of Solomon.
3. Whereas the first Greek translation of the Old Testament chose “eis” for the Hebrew "le" in Psalm 72, so that it reads: about Solomon, in the case of the Song of Songs it chose “tōi,” so that it reads: of Solomon. The Latin translation of the Septuagint followed this choice, as did the (Dutch) Dort Bible and a few English translations.
Arguments against this view:
1. Even though the Hebrew word “le” generally means of, it often takes on the meaning to, such as to the choirmaster
(Psalm 4:1 – 6:10, etc.). John Calvin already knew that this Hebrew word had many different meanings (see his commentary on Psalm 72). Very often it can mean about or concerning, as in Jeremiah 23:9; Jeremiah 49:23; Jeremiah 49:7 and Jeremiah 49:28.
2. There are good arguments to read the header above Psalm 72 as: A Psalm about Solomon.
3. In the header of the Song of Songs, the Hebrew preposition “le” is preceded by a word that introduces a relative clause. This is rather exceptional, and it underlines why we should translate le as concerning or relating to.
4. The annotations of the (Dutch) Dort Bible acknowledge that linguistically the word “le” in the Song of Songs is problematic, and that it could also have been translated as concerning. The annotators connect this to their exegesis that through Solomon we should regard this song as pertaining to Jesus Christ. However, even when we do not share this exegesis, the recognition remains that the header above this song would indicate a song concerning Solomon.
5. Solomon is mentioned a few times in this song, however, always in such a way that it would be rather surprising and unlikely that he himself would also have been the composer of this song (see e.g., Song of Solomon 1:5; Song of Solomon 3:6–11; Song of Solomon 6:12).
6. In Song of Solomon 8:11–12 one of the main characters in this book even distances himself from Solomon. In the metaphor of the vineyard, he may be speaking of the women of the king’s harem—1,000 of them! However, with his one vineyard (betrothed/wife), he considers himself richer than King Solomon.
Interpretation 2: The Song of Songs is a Song concerning Solomon.
Arguments in favour of this view:
1. The arguments against interpretation 1.
2. Overall, this song bears the character of a protest song against the sexual lifestyle of King Solomon during his later years.
The most plausible interpretation:
Interpretation 2
1 The Song of Songs, which is Solomon’s.