The Tsar bomb released an energy of $240 \mathrm{PJ}$ .
The sun releases an energy of $10^{26} \mathrm{J}$ per second.
That means there is a difference of $10^{9}$$9$ orders of magnitude (supposing that the bomb released all it energy in a second), so the effect is negigible.
It's like comparing the output of a coal power plant and a microwave oven.