Nicolas Cage's Son & Baby Mama Slapped with Eviction Notice ... Pay Up & Get Out!

The family that stiffs the landlord together, gets evicted together -- just ask Nic Cage's ex-GF and their son Weston ... whose landlord is suing to give 'em the boot, TMZ has learned.

The landlord, John R. Gifford, filed court docs to force Weston and his mom, Christina Fulton, out of their West Hollywood home ... because Gifford claims they stopped paying the $6k/month rent back in December.

Gifford says he served them an eviction notice in January, and gave them 3 days to pay up or get the hell out. Guess which one they chose?

Gifford is suing, not only for eviction ... but for the $12,000 in past-due rent.