Raven B. answered 12/28/19
Experienced Professor of Audio and Music Production Educator
So first off the cabinet type does not have anything to do with the amp power needed to power the sub... ported has to do with how the sub will interact with the room it in, it is an important aspect of the sound but not having anything to do with amplifier power needed.
The only real factor in determining the amp power needed are the driver elements inside the sub itself.
The simplest sub will have only one driver element in it, and for simplicity sake I'm only going to deal with one driver element, because as soon as your dealing with multiple drivers the whole subject quickly balloons out of control.
last of the pre-info: it is a good piece of knowledge to remember that once you turn any [low to mid quality] amplifier past 50% you are introducing noise into the signal... remember its easy to turn an amp down its not a good idea to over push the amp....so always go for overpower vs under-power.
now... any speaker driver has a couple of important pieces of info associated with it..... the three biggies are:
general Ohm ratting (resistance, usually 4 or 8, rarely 16 but sometimes possible)
RMS power
Peak power
amplifiers are also rated with the same specs....
Now here is where many professional opinions differ.....
some would say you want an amp with its RMS power level to be approx around your drivers Peak power level....
others would say twice the driver peak handling is your target RMS power of your amp (especially when dealing with powering a sub)
but what you NEVER want to do is not have ENOUGH power... an overdrive amplifier sounds awful and pushing the amp to just barley use the drivers can easily damage the drivers! Its a very simple matter to turn down your amplifier to not blow the drivers!
Now HERE IS THE MOST important bit....
WHEN the OHMs change SO DOES THE WATTAGE!!!!!!
If you are unsure about it, simple answer is to match your amps OHMs to the driver's expected OHMs....
If this isn't possible then a good rule of thumb is to assume that when the OHMs double, the wattage delivered cuts in half and vice versa... but its a lot more complicated then that... at least you won't destroy equipment if you stick to that rule... (example below)
AMP LOAD
400W @ 8 Ω <===> same if driver is 8 Ω
===> 800W if driver is 4 Ω
===> 200W if driver is 16 Ω
note this doesn't even begin to fully address the scope of the question but its a good place to start,