Can you tell us if it actually has spines (or thorns)? Because, from here, it looks like a Euphorbia. Can you tell us how many ribs it has? If you poke it, does it bleed white sap/latex? I imagine it would've done this at some point while repotting-if it is a Euphorb.

That is a nice, big specimen. I'm not the one to explain how to cut & root them, though. Hoping someone else will. =)

rosemariero, it has small thorns all over it. I will post a closer photo that will hopefully help. I will admit, I'm not sure what the "ribs" are (still learning!). When we repotted it, there was one spot where a white, almost milky liquid came out. I suspect that was the sap/latex. Hopefully that answers your question :)

Okay, as I suspected, it is a Euphorbia (a succulent, not a cactus). The "ribs" I ask about are the protrusions that run the length of the plant. From this second pic, it looks like 3 ribs.

I believe your plant is Euphorbia trigona. It is a good idea that you read up on the milky sap/latex & handling of it, so you take precautions when handling it. Avoid getting it on your skin or in any mucous membranes. Many folks have had adverse reactions to it (I am not one of them). Better safe than sorry. Wear gloves, long-sleeved clothing, etc. Seems you did a good job of repotting it without any mishaps!

Here is a link that might be useful: {{gwi:561020}}

They are pretty easy to root. Take a cutting and let the end callus over for a few days. If the sap is very bothersome when making a cut I've heard that using rubbing alcohol will stop the oozing but I've never tried it.
Pot it up after a few days. Don't water. Don't water for a few weeks. Then water sparingly. It is helpful to use a fast draining soil. When you see that it has started to grow then you can water more but not to excess.
Good luck! (Love euphorbias)

When making a cutting of Euphorbia, I have found simply washing both ends of the cut with copious amounts of water works nicely. If you want, rub the new cut end in dirt. A cutting as large as you would be making should callous at least a week to 10 days. Place the in a shaded area. You may want some rocks to support a tall cutting from falling over.

Probably the most important thing about working with Euphorbia is to keep in mind the latex "sap" is caustic to human skin, especially the facial area, eyes, etc. Wear gloves or wash frequently. Trust me the rash is very uncomfortable and lasts longer than you want!!!!

Howard

Thank you all so much! Very helpful information from you all :) I will definitely read up on it more now that y'all have helped me identify it! It seems to be happy in its new, and bigger, home. I may try my hand at cutting a little piece off and starting a second one.

Thank you all again! Truly appreciate it :)

if you would like to send me a piece off this plant, you are more than welcome!!!!!!!!!!!!!!!!!