If we had no sun, it would get so cold the entire oceans would freeze solid and it would be close to impossible for anything to be able to survive. But don't worry, it will be more than a billion years before that happens so we will destroy the earth or each other way before he sun burns out.
Some life living at the bottom of the ocean do not use the sun they get all of there energy from geothermal stuff from the core so the will still have warmth we would survive 5 min the time it takes for the sun light to reach the earth
Find the short story "A Bucket of Air," a science fiction story about this event. It would get so cold the air would freeze and the earth would be covered with liquid oxygen. Nothing would survive for very long.