Q:

Why does excel's content change when its password is modified?

I tested it by assigning an excel a password. This excel was kept in dropbox, and as I assigned a password to the excel, it was entirely downloaded on every comp that it was shared with. Is there a way that I assign the password and the whole file does not get modified? I am sure that it is not an issue with Dropbox as this is what happened with SugarSync as well.

A:

Without deeper knowledge of the internals I still would say NO - Excel has to store your password for this file SOMEHOW, so I'll guess it will be encrypted and stored within your file, hence binary changing it.
Just so you can check this for yourself:
Make a new Workbook and save it.
Open it, just password protect it, and save it as another Workbook (like the first time)
Now compare those with any HEX or Binary-Comparing tool.

