Yes. Eventually.
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But not in a long, long time. Nothing is permanent in the Universe. Nothing lasts forever. The Universe was born 13.75 billion years ago (433.6 x 1015 = 13 750 000 000) and it will live very long, yet unclear amount of time forward. The Solar System and the Earth were born 4.54 billion years ago (4.54 × 109 = 4 540 000 000). The Sun gives light and warmth which are necessities of maintaining life on Earth. Sun is a star and stars use nuclear reaction (fission and fusion) in their cores to change elements to another. Sun uses hydrogen and transforms it to helium which creates massive amounts of energy. That gives the light and warmth of a star. When all the hydrogen is transformed into helium, Sun will enlarge to Red Giant, which is much bigger star than its now, and red in colour. Red Giant is so much larger than Sun now, accordingly much closer to Earth, so it will make living on Earth impossible. It comes so hot in here that everything will burn. If Sun doesn't devour Earth itself, it will burn it to dry rock. When Sun has thus used all its left powers, and blow its utmost gas spheres out to the space, it will shrink to a White Dwarf, which is relatively cold core of a star which lights just a little white light and doesn't really produce much warmth. The Solar System will get even colder place then and life in it would be impossible.
This end of Sun and life on Earth will take place just after 5 billion years (5 000 000 000). Sun is now in the middle of its life.
Although scientists have supposed that human species will be extinct in about 5 million years (5 000 000). So we won’t be here to see the Earth destroying.
