Why is the Fermi Constant sometimes listed in units of 'joule metre$^3$'? How is that related to its normal units of GeV$^{-2}$ or J$^{-2}$? Normally, the Fermi Constant is valued as $1.1663787\times10^{-5}$ GeV$^{-2}$ or its equivalent in Joules. But on Rampfesthudson and Oxford Reference, it says,
$1.435\times10^{-36}$ joule metre$^3$
I have no idea how to interpret this, or its relation to the other units.
 A: The concept is easy, but the order of magnitude proffered is puzzling… Your puzzlement is quite warranted.
This is not an answer, because
$$ G_F=    1.16...  \times 10^{-5} \textrm{GeV}^{-2}(\hbar c)^3  .$$
Now, since $\hbar c\sim 0.197$GeV fm, you get
$$ G_F=    1.16...  \times 0.197^3\times 10^{-5} \textrm{GeV fm}^3  \\
=  1.16...  \times 0.197^3\times 1.6...\times  10^{-15} \textrm{ J fm}^3  \\ \sim 1.4... \times  10^{-17} \textrm{ J fm}^3  .$$
It would all make sense, but we are 26 orders of magnitude away...
The numerical agreement makes me suspect your sources have had a typo, which has propagated to websites. Unfortunately, 26 is not divisible by 9, so I cannot see a typo in their units, mm instead of m and such... I might have made a mistake, but they  likely have, instead.  I emailed them to clean up their act.

*

*The greater point to be made is that nobody in his right mind would do absolutely anything with the SI number.

A: In references used by physicists, such as the Particle Data Group summary (pdf link) or the NIST frontend to the CODATA recommended values or even Wikipedia, one finds the “reduced Fermi constant”
$$
G^0_F = \frac{G_F}{(\hbar c)^3} \approx 1.16\times 10^{-5} \,\mathrm{GeV}^{-2}
$$
If you invert this for $G_F$ and convert to SI units, you get
$$
G_F = G_F^0 (\hbar c)^3 \approx 1.4\times10^{-62}\,\mathrm{J\,m^3}
$$
This is different from the value in your references because your references are wrong.  I’m a little surprised to see the wrong value in the Oxford reference, which claims to be copied from the Oxford Dictionary Of Physics (6th edition, 2009), but perhaps the error has been corrected in the 8th edition (2019).  I’m also a little surprised that Oxford reference is the first result for “Fermi constant” in two different search engines.  I suppose that actually doing a computation with the Fermi constant is sophisticated enough that it doesn’t appear in most references aimed at undergraduates.
However, given that state of affairs, I am unsurprised that the wrong value has propagated to Rampfesthudson.  That site doesn’t appear to be a real reference site, but rather a content farm.  The link in your question doesn’t even show me an article about the Fermi constant, but instead articles about search engine optimization, writing college essays, whether to buy used networking equipment, and how to invest in a lawnmower.  If that site tells you some value for the Fermi constant, it is from the first search engine result at the time the article was written.  Content farms are garbage and you should ignore them.
