The Eagles Twenty One, off Desperado:
Twenty one and strong as I can be
I know what freedom means to me
And I can’t give a reason why
I should ever want to die
Ladytron’s 2002 single, Seventeen.
The lyric: “They only want you when you’re 17 / When you’re 21, you’re no fun”
I believe the song was written on Delores’ 21st birthday, so I’d say it was about turning 21.
Lost Highway by Hank Williams
I was just a lad
Nearly 22 *
Neither good nor bad
Just a kid like you
But now I’m lost
Too late to pray
Lord I’ve paid the cost
On the lost highway
*nearly 22, so he’s still 21
“Time To Be Your 21” Alexz Johnson
That was actually the first thing I thought of.
You get confused every da-ay! 
The Adverts - No Time To Be 21
Sinead O’Connor’s song “The Emperor’s New Clothes” is about how messed up she was when she was 21. Contains the line: “How could I possibly know what I want when I was only 21?”