Let's be honest (no, I am not Anderson Cooper)....many plebes have birthdays over the summer. Will a plebe get attention? Possibly, but it isn't that big of a deal and it isn't going to last long. You get MORE ATTENTION for not knowing your rates, physically unfit, or non-team player.
I am not sure what is/isn't allowed these days, in regards to cookies, cakes, etc. (probably not allowed), however, you would stand out more if you didn't send enough of something than the fact it is your birthday.
You aren't going to be mistreated, you aren't going to be dropped for pushups, etc. You DO NEED to learn to laugh at yourself, especially with some of your mistakes or you will find plebe summer that more difficult.
I had to sing a song (based off a nickname someone wrote on the envelope of a letter) to my entire squad at a meal....was it embarassing? Of course! However, it is something I can look back at and laugh on, especially with other classmates -- it is TRULY what makes plebe summer a UNIQUE EXPERIENCE!
You can't always live in fear!