Population density (on a national scale) is not relevant. Sweden is an urbanized country, like most (all?) of the western world. More than 85% of Swedes live in urban environments: https://www.statista.com/statistics/455935/urbanization-in-s...
So, assuming 3 areas 1,000 square miles with 2,000 people, 100 square miles with 4,000 people and 10 square miles with 8,000 people you do : (2,000^2/1,000 + 4,000^2/100 + 8,000^2/10) / (2,000 + 4,000 + 8,000) = 468.8 people per square mile, not (2,000 + 4,000 + 8,000) / (1,000 + 100 + 10) = 12.6 people per square mile.
The reason is adding a huge area that nobody lived in (ex: 1 person across 1 million square miles) doesn’t change the calculation. (1^2/1,000,000 + 2,000^2/1,000 + 4,000^2/100 + 8,000^2/10) / (1+2,000 + 4,000 + 8,000) = 468.8 people per square mile
Go look at a Google street view of the far ends of Stockholm metro area…
Stockholm’s urban area of 11,000/sq mi across 147.35 sq mi, is comparable to Paris, but it’s inner core 73 sq mi is a much lower density 13,000/sq mi. Even if you assumed all those people lived in a 40 square mile “inner inner” core you still don’t get close to 53,000/sq mi.