Well I am afraid, yes cervical cancer is contagious. Men can get it from an affected female during unprotected sexual intercourse. This is probably the only kind of cancer which is contagious, because human papillomavirus (HPV) is responsible for it.
No, men cannot spread any kind of cancer. Nor can women. It is not an infectious disease.
What can be spread through sexual contact is the Human Papilloma Virus, which is responsible for about 80% of all cervical cancers. There are a lot of different HPV strains, and all of them could be spread through unprotected sex.
So, men could catch HPV from an infected woman (or man, for that matter) and spread it to someone else. HPV of any kind is unlikely (very, very unlikely) to cause any kind of problem for men, except in the case where it causes genital warts (which is not cancer).
