Retrieve Google Chrome Ubuntu favicon

If you type about:cache in the address bar of Google Chrome and hit enter, you'll get a page of the items stored in cache. You can then use control+F to search for "favico". You can then copy and paste the relevant url into a new tab to load the favicon and then save it to your disk using control+S.

Edit: If you want to recover "favicons" corresponding to bookmarks, first export the bookmarks using Wrench, Bookmarks, Bookmark Manager, Organize, and Export Bookmarks to HTML file. Now, open the exported HTML file with a text editor like gedit or Geany. Inspect the file for the bookmark of interest. Here is an example of an entry in my exported bookmarks.html file:

<DT><A HREF="https://wiki.ubuntu.com/BasicSecurity" ADD_DATE="1320507266" ICON="data:image/png;base64,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">BasicSecurity - Ubuntu Wiki</A>

Note the ICON="data:image/png;base64. In other words, the favicon image is stored as a data URI. Copy the contents between the double quotes that follow ICON= and that precede >BasicSecurity (exclude the quotes) and paste it into the address bar of Chrome or Firefox and hit enter to view the favicon as an image. The image can be saved as usual by right-clicking and choosing save image as ...

You don't need a net connection for this or even the browser's cache.

I should mention that the answer was based on Kari's answer over here.

Export your bookmarks to the desktop. Open the bookmarks file in notepad. The structure is self-explanatory once you study the file. The long streams of random characters are the image data for each favicon.