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My immediate response was to do the same calc. But using SI units, because I don't live in Myanmar or the USA.
I figure that it's a cube, and judging by the size of the lucky winner, I would guess that the sides are 1.5m. 3.375m^3 at 19.254 g/cm^3 is roughly 65 tons. According to https://www.metal.com/Tungsten/202212260004 tungsten bars are trading for 49USD/kg. IDK where you got 340 USD/ton, but we seem to differ.
65 tons at 49 USD/kg is 3'185'000 USD.
I'd say that a solid homogeneous of tungsten should probably fetch a fair bit more than my price. Casting a cube like that is not going to be easy. Tungsten is rather reactive in the molten form, and has to be kept from air. Just alone keeping 65 tons of molten tungsten under a protective layer of inergen gas is going to be challenging.
No idea why the difference in price. I checked again and it still shows $340/ton on a UK site, another shows $335/ton, some higher for powders or carbide, some way lower for scrap.