Would one cycle of cypionate testosterone be sufficient enough to cause hair loss? or any other side effects. the dosage is 1 ml once a week.

Unlikely: It is unlikely that one dose of testosterone would do very much either positive or negative. The more important question is: should you be taking it at all? At your age, it is rare to see men with truly low testosterone. You should be evaluated by an endocrinologist. Taking testosterone long term causes dependency (your own body stops making it), and may cause a higher cardiovascular risk.