How long could the Earth sustain life?

Suppose the sun were to just vanish. What would happen? The sun is approximately 93,000,000 miles away, which means that it would be nearly 8 1/2 minutes before we would even know that it was gone. After that would we have any chance of survival? Could we tap the heat from the Earth’s core and live underground? If so, there is the issue of food and water. Any thoughts?