Well, first I assumed the earth’s radius is about 4,000 miles (got that number from google).
I subtracted the volume of a sphere of radius 4000 miles from the volume of a sphere of 4002 miles (water two miles deep on existing surface).
This came to about 402,000,000 cubic miles.
Then I made a mistake converting to cubic feet, and SHOULD have gotten 5.922EE19 cubic feet, which at 7.48 gallons/cubic foot would result in 4.42EE20 Gallons, instead of my previous answer.
So, the “correct” answer would actually be even more than my original computation indicated.
So, a lot of water...
:)