Both interpretations are possible. But in this case, it may be 'song of the sun'. There was a movie of such title.
Both '太陽' and '日' are used very often. You can say 'taiyou no hikari', 'hi no hikari' for sunshine.
Because 'Hi' is too short, we tend to use 'Taiyou' in order to clarify the meaning, and adjust the rhythm.
The usage of 'Taiyou(大洋)' is rather limited. 'Umi(海)' is more common word. We use 大洋 only in special ocasion.
I believe that most of Japanese imagine the sun from the word Taiyou.