For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
If the only apostle whose death the Bible records is James, I would like to
know where I can read the records of the deaths of the other apostles whose deaths are mentioned in the above question, since they are not recorded in the bible, and since they are not recorded in biblical scripture, how can we be certain of their veracity?
While historical sources might not reach the level of 'inspired scripture', there are other accounts that let us know what happened to the apostles.
Fox's Book of Martyrs is a good place to look for historically-backed accounts of the deaths of martyrs.
Here also is a good article about the deaths of the apostles: http://www.whatchristianswanttoknow.com/how-did-the-12-apostles-die-a-bible-study/