Explanation

• The energy received from the sun on earth is proportional to the square of the temperature of the sun (Stefan-Boltzmann law). If the temperature of the sun is doubled, the energy received on earth will increase by a factor of 2^2 = 4. 
• However, since the energy is also proportional to the square of the radius of the sun, and the radius remains constant, the total increase in energy received is 4^2 = 16.
• So, if the temperature of the sun is doubled, the rate of energy received on earth will be increased by a factor of 16.