Short answer: Not really.
Longer answer: a trip into Taipei center is doable on an 8 hour layover. but assuming the '8 hours' is from landing to take-off, you would need to allow perhaps 90 minutes for immigration and security (both ways), and 2 hours for transit. That would leave you with about 3-4 hours in the city.
You don't mention the time of day that you will be there, assuming that it's daytime, then I think a little city excursion would be fun.
You also don't say if you have been to Taipei before. I may get flamed for saying this, but Taipei is not rich in culture or history. On the other food is incredible. I would pick an area with shops and restaurants to explore and taste on foot. Depending upon how far it is from Taipei Main Station, you might consider using a taxi to get there, in order to optimize your time. There is a branch of the famous Din Tai Fung soup dumpling restaurant about 15 minutes walk from Taipei Main Station (It's in the Mitsukoshi Nanxi store). And there is a Tim Ho Wan dumpling outlet close to Main Station as well.
For more history, and general people watching, you could also go to Chiang Kai-shek Memorial Hall.
In closing: I certainly don't recommend passing 8 hours in TPE airport. It's just not that interesting.