Question

Why is the sun burns with fire even there is no oxygen in the space

Answer 1

The burning that a star does, then, is a nuclear reaction, and not a chemical one like the fires on Earth (when a candle burns, the atoms themselves remain unchanged: just the molecules are affected). ... So, the Sun can "burn" hydrogen to helium without the need for oxygen.

Answer 2

Sun burns because of the fusion of various gasses present in it such as hydrogen and methane.

A chemical reaction happens inside the sun which produces heat. Thus , it don't require oxygen even it is burning.