Can you get cervical cancer if you and your boyfriend had only been with each other?

No: If, and that's a big if, both partners have never had sex with anyone else, then the hpv virus will not have been contracted, and thus will not lead to the risk (by no means is it a certainty) of cervical cancer. But there is no simple means of being sure that your boyfriend is being candid about his prior exposure.

HPV: Cervical cancer is caused by hpv. Hpv is transmitted by contact. If your boyfriend got hpv from some one else you could get it. If you get a high risk hpv, you could develop cervical cancer.