I can't speak for this estimate in particular, but Verne usually did his (quite extensive) calculations in metric units. Many older translations of his work swapped in imperial or US customary units without adjusting the values for the 'benefit' of English-speaking readers.

Aha, that might actually explain the inconsistency between the volume and weight. Imagine that the volume was originally stated as 3.6 billion cubic kilometers, which would actually weigh around "three quintillion tons" (actually close to four, but let's forgive that). A translator might have turned that into 2.25 billion cubic miles, thinking that one mile = 1.6 kilometers. But of course, non-mathematical types usually don't notice that one cubic mile = 4.1 cubic kilometers.

I've looked up the original text and it uses the same units except for the weight which is expressed in "tonneaux" instead of metric tons: "[...] dont le poids serait de trois quintillions de tonneaux." So they basically swapped the units without bothering to calculate the correct value.

Now how much a tonneau weights is left as an exercise to the reader...