Much as I hate the horrible pink slimebaby
it's worth mentioning Alien:Resurrection.
When the captured xenomorphs kill one of their number in order to use its corrosive blood to escape the cell.
I'd argue that this shows they are capable of advanced tactics and understand their environment and its weaknesses.
I'm willing to concede that it's no guarantee that they understand the concept of electricity...
but I think we can safely say over the series that the xenomorphs are not animals as Hudson would mean it, as they possess cunning and intelligence.
That they'd understand that destroying cables means the lights go out, it's not that far fetched.
scifi.stackexchange.com/users/95897/Doomfrost
Ordinary xenomorph drones are shown to have an understanding of cause-and-effect, as demonstrated in
Alien: Resurrection
when first they slaughter one of their kin to escape their confinement, then turn the liquid nitrogen that's been used to control them against their captors.
However I do not believe that understanding extends to lights and electrical wires, because the drones have not demonstrated this "ability" at any other time in the series, even at times when it would have been extremely useful/advantageous to do so.
While they can see that pressing a switch performs an action, they have no way to know or intuit that said switch is connected to the light by a wire and that the wire is what makes it all work.
It is true that the drones have, at the time of Aliens , been alive for far longer than most xenomorphs in the series, and as such they could have observed humans performing maintenance-related work involving wiring and drawn the association from there.
In Resurrection it is possible drones could have been exposed to an experiment that e.g. put two simple circuits next to each other, then broke the wire of one to demonstrate that the light goes out - but of course that occurs after the events of Aliens .
In my opinion, the lights going out on the Marines is due to one of two things:
Hadley's Hope was already pretty smashed up from the desperate battle between the colonists and xenomorphs.
The power supply in that sector could have been quite literally connected by a thread that just happened to part at that moment, or was parted by the drones encroaching on the Marines' position.
Interference (directly or indirectly) by the xenomorph queen.
Queens have consistently been demonstrated to be far more intelligent than their drones (for example the queen from Aliens was able to control the elevator and stow away on the dropship),
so it's no long stretch to consider that the queen either sabotaged the power at the most opportune time, or instructed one of her drones to do so.
The second feels like the most likely explanation, and the unofficial wiki seems to agree with this assessment.
So yes, the xenomorphs did intentionally cut the power, but it was most likely the queen and not the drones responsible for doing so.
scifi.stackexchange.com/users/33266/Ian Kemp
In the Alien vs Predator (1999) video game, many of the Alien levels had you intentionally and methodically sabotage things to disable power or get access to targets.
If that is considered canonical I would say it shows they do.
scifi.stackexchange.com/users/24007/Servitor
Also remember that the main reactor in the Terraforming plant was about to blow.
Was this the main power for the whole planet?
Unknown, but it was connected to the base for monitoring.
Perhaps a huge surge from the plant caused the base breakers to blow.
In the final scenes, the entire facility is throwing all sorts of electrical emissions as the reactor goes critical.
That kind of activity could produce an EMP large enough to knock out a building.
scifi.stackexchange.com/users/26266/GeorgeN
No, they did not do it deliberately.
The xenomorphs do not attack for about three minutes after the power goes down, and only attack after being discovered and shot at.
Any element of surprise they might have been hoping for is completely squandered by taking so long.
They would have done better if the power had not been cut at all.
However, it is likely that they cut the power accidentally, rather than the power station failing, as the loss of power seems to be local.
The backup lighting is red, which for some reason exists even in the air ducts(?).
When Ripley & Co move on the lighting in the rest of the facility is much the same as before the power cut, with white lights everywhere.
The xenomorphs were in the overhead spaces, which is a logical place to put power cables and a logical place for xenomorphs to trip over them.
scifi.stackexchange.com/users/83770/James Hollis
It can have a very easy explanation that is somewhat relatable to the real world: beasts simply attack everything that vibrates or emits warmth.
This behavior sometimes feels as if it is devilishly intentional, and this can be confirmed by any farmer who had to deal with mice in his shed.
But it is just a coincidence: all animals seek warmth, and predator animals seek sources of sound, while our technology tends to emit most of those at its weak points.
The only intelligent thing I can remember is their tendency to hide in escape vehicles right before they launch, and not to attack crew until they land.
In the trash comedy "Tremors" this behavior is displayed in detail: monsters leave a town without communication and vehicles because they stupidly attack everything that is warm or vibrates.
scifi.stackexchange.com/users/31432/Barafu Albino
I figure deliberately.
If I am going to design a living weapon like the aliens, smarts would be a key ingredient.
The eggs were located in a spaceship and it would be prudent to have the spawn understand the concept and running of the ship.
Like the other poster said, a better example is the queen making the conscious effort to follow Ridley into space without revealing her presence in order to survive.
It she was just trying to get revenge, she would have attacked the shuttle immediately.
The same in Alien.
scifi.stackexchange.com/users/99277/John Pombrio
In Aliens, the marines have fortified a position and are preparing for a last stand when the power suddenly goes out. Hudson appropriately asks, "How can they cut the power, man? They're animals!"  Later, we see that    the xenomorphs have crawled through the drop-ceiling.   Did the xenomorphs intentionally cut the power as a combat tactic, or did they    just kick something when crawling around?
Did the xenomorphs intentionally cut the power?
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<alien-franchise><aliens-1986>
scifi.stackexchange.com/questions/185660
scifi.stackexchange.com/users/75432/Tashus
There is no agreement as to whether the xenomorphs cut off the power deliberately or even if they did it at all. It would not be far-fetched to suggest that they understood the mechanisms to cut the power, but there is no evidence to suggest this. The power outage could have simply been caused by something else, such as a power surge. This is a matter of interpretation - there is evidence that xenomorphs possess sufficient intelligence to deliberately cut the cables but equally they may have severed them accidentally as they crept through the overhead space.
In Alien:Resurrection the captured xenomorphs kill one of their number to use its corrosive blood to escape their cell so they do possess intelligence of a kind and therefore they could have understood that destroying cables means the lights go out. There's no way they could have understood that the lights would go out if they destroyed the cables - the power supply was probably hanging by a thread and then failed for other reasons. The base breakers might have blown due to a power surge from the plant. They did not do it deliberately - if they had have then they would've attacked immediately and not waited 3 minutes. Perhaps they just tripped over the cables and snapped them. Perhaps they instinctively bit through the cables because they were warm - like a mouse does. It was deliberate - they were designed to be a weapon so it is logical that they would be given enough intelligence to see something like this.