I have two huskies which is a breed known for its high prey drive, but I am able to keep everyone in line and under control. Of course you won't be able to in this case, but it is always a good idea to socialize young puppies and kittens to all sorts of different animals and experiences when they are young so as to avoid potential problems, especially with large breeds.
Anyway, my dogs would certainly go after Savannah if given the opportunity, though they know to keep their distance after a little bit of training. They have both had a lot of obedience training and know to stay put when Savannah is on the ground. Otherwise, she is up where they can't get to her. When we first brought her home they were much more curious and interested in her but now they only roam over to her cage to eat the scraps she drops.
Growing up, we had a Sun Conure along with two cats and two dogs. The cats were hunters and had been known to catch birds here and there. Other than watching him, they left the Conure alone. They seemed to know the difference. But, you can also train cats. Loud noises, spray bottles, or strategic placing of tape is a good way to deter any cat.
It is best to have a cage where the animals can't get to the bird. I have a floor cage that has legs taller than my dogs. The legs combined with seed catchers make cage sniffing impossible for the dogs unless they jump up. For you, possibly a hanging cage or a tall floor cage would work. Make sure to not place the cage near any surfaces the cats can jump up and attack through the bars until you are positive they will not.
If you have no option other than to place the cage on a surface or near a table/counter then I would suggest putting a few pieces of duck tape upside down so that when/if the cats jump up they will almost immediately regret it. Cats are smart and will learn very fast. You could also place tin foil on the surface, or on top the cage(if you think they will get on top, as some cats are scared by the noise. Spraying them is also an option to punish negative behaviors. Though i don't find it as useful.
It is possible but you have to be willing to put the time and effort in to train the animals to exist happily together. Sorry this is so long. Hope it makes sense.