What program should I use to open .db3 files? I have a series of .db3 files in my computer. They are like filename1.db3, filename2.db3, filename3.db3, filename4.db3 and so on.

I can open filename1.db3 with sqlite editor. But when I open filename2.db3 file with sqlite editor, the sqlite editor gave me error like "It is not correct format". 

What program should I use to open all of those .db3 files together? Thanks in advance.
In theory you should know where the file came from and ask the person who gave it to you. A file extension could mean anything. In the old days, .db3 extension used to be for dBase III data files. It also could be for SQLLite binary dump file. See for example Importing SQLite db3 files. If you have problems, it may be attributed to many factors, version compatibility may be one of them. You may also want to perform an integrity check as in here:Pragma Check.