Twice the area of a 20-foot cube is two 20-foot cubes
I'm afraid this is one of those "There is no raw answer". So, we rely on a handful of "hints" from the devs until we get an official answer. The most relevant hint here to me is "plain text interpretation".
The book doesn't give any guidance I could find about doubling areas, at least not in this way. Normally, I'd pull up some definitions, but entries for words like "size" or "twice" aren't super helpful here.
Size (for example)
the relative extent of something; a thing's overall dimensions or
magnitude; how big something is
The only course of action left is to decide upon the simplest and easiest to implement option.
Question: How many is one 20 foot cube?
Question: How many is twice of one?
Two twenty-foot cubes... or a 20ft long, 20ft high, 40ft wide rectangular prism. Whichever.
I also realize that the spell says: (emphasis mine)
The web created by the spell fills twice its normal area.
An argument can be made that they're telling us to double the ground area, which supports my answer.
The possibilities (from most to least likely in my view):
Twice the volume, but keep the height at 20
This is the most literal and simple to understand reading. This gives you either a shape that is 20x20x40, or if it is still a square, about 30 feet to a side (technically 28.28). This is also the same as doubling the area.
Twice the side length
We go from a 20 foot cube to a 40 foot cube. This is the easiest to envision, in my opinion. That gives us 64000 cubic feet of volume. You and I both know that 40 foot cube is much more than twice the volume of a 20 foot cube. But D&D is not a great reality simulator and it's an even worse math lesson.
Twice the volume (from the center)
A 20 foot cube is 8000 cubic feet. Twice that is 16000 cubic feet. The cube-root of 16000 gives us about 25 feet to a side.
Twice the side length, but keep the height at 20
20x40x40 gives us 32000 cubic feet.