The sun will never blow up the way we think of a genuine explosion. The Sun will blow away most of its outer layers. In fact, the Sun is doing a slow-motion explosion. At the moment the Sun gets its energy from turning hydrogen into helium. When the Sun's hydrogen runs out in the hot and dense center, then the Sun will expand into a red giant, about 100 times bigger than it is now, and will start turning helium into carbon in the center, and hydrogen into helium in a shell around the center. This phase will last about ONE THOUSAND MILLION YEARS.

The Sun will die and turn into a "white dwarf", and will no longer generate energy, but will very slowly cool down for the rest of its days. A white dwarf results when a low or medium mass star dies.

On the other hand, if the Sun loses energy and size, the planets will no longer be orbiting around it, but they will not have a reason to blow up. The process of the Sun losing energy and size will be really slow, and the effects on the planets will be slow, too.