It takes 8 minutes for the light to travel from the sun to Earth. Because light in a vacuum travels faster than anything, including information, we would not and could not know it had disappeared for 8 minutes. This means Earth would continue to follow its orbit around a non-existent sun for 8 minutes because the Sun’s gravity would still be acting on the Earth.

If it was nighttime, you wouldn’t notice the sudden lack of sunlight (other than if it was a full moon) but you’d almost certainly notice the change in gravity.

Edit: actually, you wouldn’t feel any difference in gravity or experience any change of acceleration. What you would experience is a very tiny vibration, of 1 million push notifications being sent to your phone from the other side of the planet.