Russia can't take out all the "internet cables." Presuming we're talking about undersea cables, there are a fuckton of them. The logistics of taking out even a handful of those before the world takes action is beyond what Russia is capable of pulling off.
Even if they do manage to cut some, traffic would slow down, not stop. Then the cables would be repaired, and everyone would be more pissed at Russia than they already are.
It's nothing more than bluff and bluster. It would be a minor setback for the world, and have huge downsides to Russia.