Basically I wonder what happens to emitted radiation by douubling a light e.g. twice the surface area of the sun will emit how much more radiation? 4 times more? Is there a formula?
If you assume a radiator (sun, lightbulb) of constant power (e.g. 60 W), you can increase its surface in any way you like (assuming the material only diffracts the radiation and doesn't absorb it), but it will always emit the same power, which is (e.g.) 60W. This is, simply, conservation of energy. It's not a matter of temperature.
If you are, on the other hand, talking about black body radiation, Wikipedia states that the emitted radiation is proportional to the surface. Double the surface, and you will double the radiation.