I'm having a problem with the vagrant when starting the box. When I give a vagrant up.
Look at github for the bugs that occur. link
Informs that it is out of date with the updated virtual box as well as the Extension Pack.
After giving the ssh vagrant I can not see the gemfile to start the server.
In the log you reported, the vagrant is looking for 32bits packages, but the repository that is configured to update the ubuntu packages only provides 64bits packages.
The next line is what appears in your log that makes me think about it:
Failed to fetch http://apt.hellobits.com/dists/trusty/Release Unable to find expected entry 'main/binary-i386/Packages' in Release file (Wrong sources.list entry or malformed file)
If you download the file indicated in the URL of the log, you will see that the repository only supplies main/binary-amd64 packages, but there are no main/binary-i386 entries.
Instead of using a 32bits box, use a 64bit. This should resolve your issue.