According to AMD the standard Radeon RX 580 card requires a total of 185w.
A Mac Pro can provide a video card with 75w from the PCIe slot, plus 75w per mini PICe cable. This means a maximum total of 75 + 75 + 75 = 225w which should be more than sufficient.
However I have seen some real life reviews of RX 580 card showing that under have use they can use over 200w of power see AMD Radeon RX 580 8GB: Power Consumption and could under extreme use exceed the 225w level.
With regards to cables, I don't have one of this model card but I am under the impression it has both a 6-pin and an 8-pin socket. As such it is designed to take 75w + 75w + 150w = 300w. This would cover even the most extreme use of the card and as per the above article cope with use that drives it higher than the 'official' 185w requirement.
The Mac Pro cannot supply 75w + 75w + 150w since it only has 6-pin power connections. Some people have cheated and used adapter cables e.g. to go from 6-pin to 8-pin but some people have then reported their Mac Pro shuts down to prevent an overload. Even if you avoid it shutting down there is a danger this excess load might literally melt the traces on the logic board supplying the power connection.
So you need to be careful, 'average' use should be ok but if your doing bitmining constantly or some other demanding task you might cause your Mac to shutdown. (Or melt.)
You can normally connect a 6-pin supply cable to an 8-pin socket, this will still only provide 75w but means you don't need an adapter. You can take two 6-pin cables and 'merge' them in to one 8-pin cable but this is going to deliver exactly the same amount of power as two 6-pin connections.
I believe this - Amazon.com: GutsParker Dual 6-Pin Female to 8-Pin Male Cable Black: Computers & Accessories is the right sort of cable to combine both 6-pins from the Mac Pro to a single 8-pin. You would use that adapter with two standard Apple mini 6-pin to normal 6-pin cables like these Amazon.com: CNCT Mini-pcie 6pin Mac-pro G5 to Pci-express 6-pin Video Card Power Cable for MAC Pro (2 PC): Home Improvem…
Remember this will only give you 75w + 75w + 75w = 225w.