Literally it says billions of billions, but in context it most likely means billions upon billions.

Why? Petabytes seems like a more likely order of magnitude than gigabytes, doesn't it?

eta: From the article: "capable of managing dozens of petaoctets of data, in other words dozens of millions of gigaoctets"

Actually 'zillions' is probably the most accurate translation.

No. The correct translation is "billions of billions"