Ok, so if you accidentally delete a file, what this effectively does is to remove the file name from the file index and mark the space associated with the file as available for use. If you stop using the system at "that" point, i.e. before the space is used up by something else, it's is generally possible to recover the data. However. What you have done is to replace your data, block for block, with new data, so on the face of it, there is nothing to recover as the data itself has been overwritten - at least for the first couple of G of data,
In terms of "how to the FBI do it?", overwriting a block on the disk could be analogous with writing something with pencil, erasing it with a rubber, then writing something new on top. What was there has gone, however with the right tools (maybe with some graphite powder etc) it may be possible to see an imprint of what was there and deduce what had previously been written. Now this relates to magnetic storage, not sure how it applies to solid state media, but either way I think it would likely require specialised (physical) tools, be expensive, and unlikely to produce very much that's usable. As far as I'm aware standard hardware can't recover overwritten blocks from any type of media.
If you think there may be data you want on the device "after" the first couple of G's, i.e. the size of the ubuntu ISO, you will need a tool that will scan your device at block level looking for valid file / directory entries .. the tool you need really depends on the filesystem that "was" on the device before it was overwritten. Were you using extfs, fat, or something else?
