* スイート シックスティーン (Suīto Shikkusutīn) This is a transliteration, simply using the English words in Japanese pronunciation. It would be understood, but sound foreign.
To convey the meaning of a 16th birthday celebration, you would be better off saying something like:
* 16歳の誕生日 (jūroku-sai no tanjōbi): 16th birthday
* 十六歳の誕生日パーティー (jūroku-sai no tanjōbi pātii): 16th birthday party
These options are much more natural and commonly used. The "sweet" aspect would need to be conveyed through the context of the celebration itself (e.g., describing it as a lovely or special party).