What will the problem be if Odysseus kills the Cyclops?

In book 9 of The Odyssey, Odysseus and his men stumble upon the land of the Cyclopes. After finding a cave filled with milk and cheese, Odysseus attempts to snatch some nourishment for himself and his men; unfortunately for these gentlemen, a Cyclops named Polyphemus returns to the cave and eats two of the men. Polyphemus, who also happens to be the son of Poseidon, places a massive boulder at the entrance of the cave, imprisoning Odysseus and the rest of the surviving men.
Since Polyphemus is a giant, only he is strong enough to move the massive boulder that seals the cave. While Polyphemus is a violent monster that consumes men, Odysseus is placed in a peculiar predicament: should he kill Polyphemus, the boulder will not be moved, and Odysseus and his men will starve to death in the cave. Yet, as time goes on, Polyphemus simply aims to continue to eat the men one by one.
Ultimately, Odysseus blinds the Cyclops with a wooden staff that was heated in the fire. The next morning, Odysseus and the rest of the men escape by clinging to the sheep that Polyphemus was keeping in the cave. As the animals leave the cave to graze, the men are able to escape.