Reading the Summer love lyrics, the lyrics go as follows: "summer love, had me a blast". I know that "have a blast" means to enjoy etc. But I do not think I could say "it has me a blast".
Even in spoken English or plain prose, we would drop pronouns - particularly I - in some situations.
Here, "had me a blast" is doing this to "I had me a blast".
"I had me" in turn is an informal variant on "I had" found in some dialects, that adds emphasis.
So, "I had a blast".
The sentence means I had me a blast.
The subject I is understood. While the reflexive me is not standard usage, the slang inclusion is used for emphasis.