There are probably some people careless enough that destroying a single data centre would damage them. Most serious contenders (e.g. My employer) have fully redundant active-active setups across regions, so you'd have to engineer a massive outage to take out real shops.
Of course, if you completely remove an entire AWS region you might induce very damaging stresses on other regions as people fail over.
Why blow up anything or damage any cables? Hack the computer of an Amazon employee and do your damage there. The last S4 outage was because of someone fat fingering a script, imagine what someone could do that really wanted to mess stuff up.
And ultimately it leads you back to targeting the IT operations centre for the business where they provision equally to say both AWS and Azure for redundancy. At that point you can knock all of the biz cloud capacity off.
Well, you need to disable redundant ISP or power cables to all datacenters in a region. and that would probably be pretty easy to recover from in a day or two.
I imagine Amazon has some on site security measures as well.
It would be interesting to see how important services would cope with their main region going down for more than a few days.
Not that I think it is wise to discuss optimising a terrorist activity on a public forum, though it is interesting from a threat analysis point of view.
You don't need to severe both power and data cables. For power the datacentre should be able to cope for a while, particularly if it has access to fuel deliveries. Data cable should be both easier to severe and more difficult to recover from (not the least to identify which cable has been cut where).
Most of the infrastructure of a country in term of cables run along railway tracks, sewers, etc. This means thousands of kilometers of cable even for a small country, and it is impossible to secure everything. It is impossible to severe everything either but you don't need to severe every single cable. As long as you severe enough of the backbone, the other cables will be overloaded.
So I don't think it would take that much effort for a network of terrorists to create havoc in the communications of a country for at least a few days to a week. And the consequences for the economy can be pretty dire. We have seen with BA what happens when their datacentre goes offline. Their all fleet is grounded. I imagine the consequences of a country-wide outage could be pretty dramatic. Unlikely anyone would die but you could really dent the GDP.
But if that's your methodology, you'd need to cut several cables in different locations simultaneously. A single cable doesn't take too long to fix (a couple hours, tops) and there are probably several redundant backups to handle bandwidth in the interim.
