Is our sun in a star cluster? Sorry for the absolute begginer question here, but is our sun a part of some globular cluster?
It is something related to Virgo supercluster?
No the sun is not part of a cluster.

There are several types of clusters that we see in the sky. The most familiar is the "open cluster", like the Pleiades. These are a group of stars that formed together and have remained close.

As the stars drift apart they can become part of a "moving group", a collection of stars that don't appear to be a cluster, but since they share the same age and direction of motion we can tell they used to be a cluster.  Many nearby stars are part of the Ursa Major moving group, but the sun is not one. It just happens to be in the same part of the Milky way. The sun was probably part of a cluster shortly after it formed (4.6 billion years ago) but that cluster has long ago broken up. We don't (yet) know of any other stars that seem to have come from the same cluster.

Globular clusters, like M13 and Omega Centauri, are larger and have many more stars tightly packed together. They are all rather distant, and the brightest look like slightly fuzzy stars (in fact Omega Centauri was originally thought to be a star).

Of course a galaxy is a group of 100 billion stars. We don't normally think of galaxies as a star cluster, because they are so much bigger and the stars in them don't form at the same time.

Then there are clusters of galaxies, the Virgo cluster is a cluster of galaxies, and the local group of galaxies is on the edge of this cluster. But the Virgo cluster is not a star cluster.