I've been reading up on this a lot as I'm thinking of restarting a reef tank. The rock you used is the same rock I have looked at. So maybe my understanding of curing is wrong, and if so I'm sure someone will chime in and correct me. Which will be good so I get a better understanding, but will probably leave me with Pukani all over my face.
This type of rock, from all the posts I have read, is full of Phosphates. It is all trapped inside the rock so a vast majority of people recommend curing the rock first. And I understand curing to be the same as cooking. This might be where I have it mixed up.
But if I'm correct, curing is basically sitting this rock in a vat/tub/trashcan of water with a pump for flow, RO/DI salt water, and waiting for it to leach out all these phosphates. The rock can cure for as little as 4 weeks and be good, or upwards of 2-3 months. Some have even gone longer. They also use a product called LC to speed up this curing process.
If you skip this step, my understanding is that in a few months you are possibly going to be dealing with a huge algae problem that could literally take a year or more to get rid of. This is just reading past experiences, so don't panic yet, it is not a definite thing, but something I really took into account so it won't happen to me.
People have cured the rock in their tank, but I think GFO was required, and from my understanding, the leaching was so great, that gets very expensive to use instead of the LC method. Problem with the LC method in a tank, it is tough to get all that stuff out. It sticks to the glass, you will be doing massive water changes to remove it, so water/salt becomes a cost factor. And since the tank isn't really completely dark you might still get some hair algae or blooms on the sand.
It really seemed like a better method to me to do this outside of the tank and since you just started, it wouldn't be to late to think about doing this.
Once all that is done, and since you went through buying the dry rock, you can have the time to build a really nice aquascape setup. This rock is easy to cut, drill, carve out caves, etc, so why not take advantage of that. You could build a structure, then cure it in a bin, when all the phosphates are pretty much gone, move it to the tank and begin the cycle. It might even halfway start the cycle inside the bins, so that is why I would recommend the aquascaping first. Just to prevent as little of the bacteria which might have come alive from dying while you have it all sitting on the floor in your design mode.
And as fur cycling, that is just the build-up of the bacteria in the rock to deal with your ammonia/nitrite/nitrate cycle. I don't think it is the same thing as curing, at least it didn't read that way to me. Two different things.
Yes, they can technically be done together in the tank, but I don't plan on taking the risk and fighting some hair algae outbreak from all the leached phosphates which are more than likely there and waiting to be set free.
But I eagerly await to see if what I read and put together in my own mind is actually right. Better to find out now than after the fact and I screw stuff up.