Is ower sun big enough to make a black hole?

The only mechanism by which black holes are known to form is the gravitational collapse of a star with a mass at least 20 times that of our Sun.

All objects require some outward force to balance gravity. In main sequence stars, the outward flow of energy from the nuclear reactions in the core creates an outward pressure to balance gravity. Once the fuel is exhausted and the core collapses, there are two more forms of pressure which can halt collapse.

First, electron degeneracy pressure, which can be thought of as a repulsion between electrons. Electron degeneracy pressure can support a body of up to approximately 1.4 times the mass of the Sun, and stars that end their life in this state are known as white dwarves.

Second, neutron degeneracy pressure; repulsion between neutrons. We are less certain about the extent to which neutron degeneracy pressure can support a body against gravitational collapse, but we understand the limit to be somewhere around 2.5 times the mass of the Sun. Stars that end in this state become neutron stars.

An object experiencing gravitational collapse which has a mass greater than can be supported by neutron degeneracy pressure will collapse into a black hole.

Note, that it is not the entire star that collapses, merely the core. The outer envelope of the star is ejected as a planetary nebula in the case of lower mass stars, and in a supernova in the case of higher mass stars.