Even if we take 1985 levels of nuclear warheads - the maximum, I believe USSR had 40 000 back then, and fuck it, lets say for even numbers, 100 000 nuclear warheads.

Land-surace is about 150 square million km. Take 1.2Mt the biggest yield in US arsenal currently. That would require around 270 000 nuclear warheads to cover every square km. We dont have that many and never had.

Also that wouldnt even scratch the oceans.

And the cobalt bomb, it hasnt been built, and anyway wouldnt work its not a doomsday device.

There are also way too many caves and cave systems with ecology in them which would be largely unaffected by civilized weapons.

Sure, the earth wouldnt look like it does today, but life would still prevail - and civilization isnt really that powerful to exterminate all life.

"...to cover every square km. We dont have that many..."

One does not have to rake every piece of soil in order to wipe out the entire life. The oceans would get the radioactive lavement of the soil and cycle that back on the land over and over though radioactive rains. This affects especially the bottom layer of the food chain, which cause chain's partial (if not total) collapse. In the end there is the possible nuclear winter that may render almost the entire planet inhabitable for all life forms. (Spores, bacteria, algae or other microscopic life forms may resist in hibernation to thrive again someday, but that is not called "living" through the event.) The reality is that there wasn't in our planet history any extinction event that involved nuclear contamination of every available living habitat (among other hostile-to-life effects), and speculating about it and about if it would or not be destructive enough, feels to me a little bit like playing with madness here.

I laugh I your General direction: http://en.m.wikipedia.org/wiki/Waterbear note there is a lot of surface area on the planet. A 1MT nuke per sqare mile would come fairly close but not quite get to where you suggest and we don't have close to that many nukes.

I have to say I love Tardigrades, but without a food source they are not going to survive. Nuclear winter is not too conducive for moss growth.

More seriously I suspect that short of a massive high altitude cobalt bomb detonation that some small life will survive on the surface even if all the current nuclear weapon were used.

Well they can go without food for 9+ years so that's more of a long term problem. As to nuclear winter they already live in Antarctica so there food source can also survive fairly harsh conditions, and it only takes one (or 2 depending on species).

Not that we have a lot of spare planets lying around but IMO it would be an interesting experement. Also, there is a fairly interesting ecosystem living inside the chernobil building which just goes to show how hardy some things are. http://en.m.wikipedia.org/wiki/Radiotrophic_fungus Gama radiation as food... Yea that's a thing.

A cobalt bomb will keep the background radiation level on the surface lethal for nearly 100 years.

There is no way we can yet destroy all life on earth - microbial life is too tough for that, but we could destroy all macroscopic life on the surface.

Excluding caves. Also, rain drastically reduces how long radiation stays in an area. And again cobalt produces Gama radiation which some things use as food.