Is there any relations between the Goths (East Germanic tribe) and Gothic (subculture)? If yes or no, explain.?

I think there sort of is between the term itself, but not the racial/cultural groups. The term "gothic" was used to describe barbaric or uncultured people (regardless of whether they were actually Germanic) from Imperial Roman times onward. The term gradually came to mean anything or any one who wasn't up to date with the culture of the time. Since modern gothic people are a bit on the fringe of modern culture, and are often greatly influenced by Victorian fashion and literature you can sort of see the way the word connects back to its origins. I reckon we could probably trace the word "vandal" back in a similar way.