I had much more success in my second attempt and was able to create a half-decent cube. I say half decent because I messed up one of the faces of it. While I was machining the second face in operation the tool suddenly popped loose, and I didn't catch it right away as it only shifted a couple of thou. I numbered each face to show the sequential order of how it was machined.
After the whole operation completed, I was able to cut it off the base as I left a small amount of material it would avoid. One huge thing I noticed was that it would shave the side face it was working on and cut it down by about 1/64", when done on each side it would make cube smaller on each face by 1/32". This may not seem like that big of a deal but when trying to get precision parts, this is pretty big. It's hard to notice from just looking at it, but with a pair of calipers, it's self-explanatory. I looked up possible solutions and may have found something here I'll look into for next time.
For the time being, it turned out pretty great aesthetically, and each face is immaculate and sharp, which was better than I could have hoped. Next, I am going to attempt to make a "perfect" cube in a single operation-perfect meaning without errors and having to shut down the machine.