The sun is said to only have a life span of about 4.5 billion more years. with that being said, will there still be life on earth, in the absence of the sun?

No because plants wouldnt be able to grow and there will be a massive power loss cause of solar panels

No, the will not be life on Earth because all plants require the sun to produce food for themselves. We require plants or animals for food (animals eat plants and if there is no sun, there are no plants) so we wouldn't have food so we would also die. That being said, there are types of bacteria and cells that live really far down in the ocean and also in caves that don't need the sun so they would still survive. Do you count then as life? Or are you only talking about animals, mammals, reptiles, etc?