By how much does the energy emitted by the sun vary?

Answer 1

The Sun loses mass radiation in proportion to the Nuclear masses it contains.The more mass it loses the less mass remains for nuclear Reactions.The less mass remains the less radiation energy is given off.
Any thing decaying in proportion to itself is therefore and exponential decaying function.
Therefore in Time the Sun will give less and less mass and energy emission.

Answer 2

The sun's energy output varies slightly over the 11-year sunspot cycle. The variation is about 0.07% for that period.