Well, look at it from her point of view mate. She has a boyfriend who is picking her up. How bad will it look to him if he sees you (her ex) giving her birthday presents when they are about to go on a trip together?
I understand your pain and frustration. It sounds like you still have feelings for her, but she's moved on now, she doesn't feel the same for you anymore. You need to move on as well and just treat her as a friend. Giving a friend a cake one day after the birthday, won't stir up the same sentimentalities in you. It sounds like you need to find a way to move on.
Don't cry, don't regret and don't blame
Weak find the whip, willing find freedom
Towards the sun, carry your name
In warm hands you are given
Ask the wind for the way
Uncertainty's gone, your path will unravel
Accept all as it is and do not blame
God or the Devil
~Born to Live - Mavrik~