I have breast cancer tumor. Went from 3cm to 5 CM after biopsy but stable since. If outer part is liquid, can it be drained by needle prior to surgery?

Drainage unnecessary. The size of the tumor does not include any bleeding from the biopsy. Therefore, if it was 3 cm before the biopsy (&the biopsy was recent), the tumor is still 3cm. You need not worry about this fluid and may proceed with your definitive surgery. I hope all goes well.
The tumor. didnt increase in size right after the biopsy, the apparent size increase was likely due to bleeding. It is unnecessary to treat this prior to surgery.
Breast Cancer. The cause of the increase in your tumor size so soon after biopsy is likely related to some bleeding after the biopsy which caused a hematoma. However, it is important that you meet with your surgeon to be reevaluated as you may be a candidate for neoadjuvant chemotherapy.