Some time ago, I read a story about first contact with aliens. The location is Earth, Humans greet the newcomers - but they only see Humans as a protein source. Whether novel or short story, I do not remember, but probably not by a living writer, somebody active in the 60s or 70s?
This sounds like the short story "Food to All Flesh" by Zenna Henderson, first published in 1953 and anthologised many times since. In this story a man wandering in the woods finds an alien creature. The creature (who I recall as somewhat catlike) shows the man its spaceship and indicates by gestures a piece of damaged equipment which produces food. The man offers food which the alien swallows and then "unswallows" when its body rejects it. Over a period of time he brings more and more samples of possible foodstuffs but in every case the result is the same.
On the final visit the alien shows the man some smaller aliens, obviously its children. They are mewling with hunger and somewhat reminiscent of kittens. The man picks one up in order to comfort it; it bites his hand and swallows a small piece of his finger. The mother takes the child and waits for it to regurgitate what it has swallowed. It does not, but instead starts to purr in contentment. The mother alien then grasps the man by the arm and looks long and hard at him, then lets him go, gets into its spaceship with its family (one fed, the rest hungry) and flies away.
Another possibility is Damon Knight's 1950 short story To Serve Man. In this story aliens arrive on Earth and bring about an era of peace and prosperity, providing clean unlimited power, abundant food, stopping war and working to prolong human life. They also offer to take humans on ten year "exchange visits" to the alien homeworld.
A character obtains a book belonging to the aliens which seems to back this up. The title of the book is translated as "How to Serve Man". However, when the first chapter of the book is translated it is found that it is a cook book.