Can the Sun become a big ball of gold atoms? The atoms inside the core of sun are continuously fusing and forming other atoms. Can this continuous fusing make gold atoms?
Gold is heavier (further down the periodic table of elements, not necessarily more dense, although this is also the case) than iron. Iron's elemental number is 26. Gold is 79.

Any star that attempts to fuse iron will go into a supernova phase.

At that point, gold and all of the elements heavier than iron will be created, but only in the brief moments while the star is tearing itself apart.

No star can ever create gold in any circumstances other than during a supernova.  Our own sun is not nearly large enough to go supernova.

Any supernova will create gold, not just the type of supernova described above.

More reading: https://en.wikipedia.org/wiki/Type_II_supernova