I know I can't use 32bits softwares in a 64bits pc, but what about within Sun Virtual Box?
Sorry! Ok, so I can, now stop voting me down! :)
As has been noted in the comments you can use 32-bit software on a 64-bit computer, with the only exception being that low-level 32-bit "kernel" drivers will not work on a 64-bit OS, typically this just means that older hardware may not work.
On the other hand you cannot use 64-bit software on a 32-bit operating system.
Speaking of Virtualbox, if you are running a 32 bit host operating system you can install a 64-bit guest operating system assuming that your processor supports it, though there are some limitations. This could allow you to run 64-bit software on a 32-bit system.
After elaboration from your comments it appears that you may be trying to install a 32-bit addon to a 64-bit web browser and that follows that same kind of restrictions as 32 bit drivers in a 64-bit OS. For Flash to work in Firefox 64-bit you'd need a 64-bit version of Flash, which Adobe have put aside for now. This is one of the main reasons that Firefox 64-bit is not common, and also why Windows 64-bit version include both 32-bit and 64-bit versions of Internet Explorer, just so that plugins that require deep integration with their host (e.g. Flash needs to get access to areas to draw objects and render video) will work on the more compatible 32-bit version of the browser.
If you are needing to use Flash then you may need to look into installing the 32-bit version of the browser you are using.
Right, just got Chromium installed on a nearly blank Ubuntu install. By default I get no videos on Youtube as they all require Flash to be installed prior to seeing anything, same goes for Firefox.
Closed Firefox and Chromium then going back into the package manager I searched for Adobe Flash and installed the one that has a proper adobe logo. Flash video now seems to work fine in both Firefox and Chromium for me. The name was "Adobe Flash plug-in" in the Software Centre.
Don't download it from the internet to install yourself, get it from the Ubuntu Software Centre, and going through Ubuntus software installer will make sure that stuff gets installed in the right place.
Going back to the 32 and 64-bit question, I'd have thought that Firefox and Chromium are both 32-bit programs on my 64-bit Ubuntu, as is the version of flash that gets installed. You can't install a 64-bit version of flash on a 32 bit browser and likewise a 32 bit version of flash won't work on a 64-bit browser.
Hmmm. Maybe I'm wrong there...
And the same for the Flash plugin...
So, it looks like on 64-bit Ubuntu you need the 64-bit version of Flash, which you can't get from Adobe as they axed it. The downloader from the Adobe website probably gets the 32-bit version of flash which will be useless on Ubuntu 64-bit, so go get it via the Software Centre and all should be well.