Just 8 minutes after the Sun went out, every corner of the Earth would be in darkness. The darkness that would be noticeable at midnight would come suddenly and without warning. The Moon would not be visible, as there would no longer be sunlight to reflect on its surface. But the real problems begin after a few hours.

The first and most critical of all for life is the complete conclusion of the process of photosynthesis by plant organisms. Without a constant production of oxygen, many forms of life on the planet are now numbered.

The second problem begins to make itself felt towards the end of the first day: temperatures have dropped significantly, and continue to drop at a rapid pace. After a month, the planet is covered in ice, reaching a temperature of -40°. The only life forms that can still resist the continuous cooling are those near geothermal activities, such as tectonic faults, geothermal springs and areas of the ocean.

Considering this scenario: current sun just “goes out”, may collapse into a white dwarf without side effects (which is NOT possible…).
We´d recognize it about 8 Minutes later (light takes this time). Not really relevant.

Then after some hours we´d experience a slowly cooling down earth – just consider a normal night. But this cooling down does not stop and continues until even the air freezes – may be 1 month into this “game”. Then we are destroyed. Only heated self-sustaining bunkers can stand this for a prolonged time – so after 1 month 99.999% of mankind died. And the rest “runs on reserve”, which may last for 1–3 years I assume. That´s it. The “finishing point” is power supply. No normal bunker is so deeep to get heated properly by the earth´s core.