Nearly a month ago I replaced my battery cables. They were corroded, weak, and nearly black from bad corrosion.

Recently I popped the hood and noticed that my positive battery terminal has begun to get chalked up with black corrosion.

Can I "chalk this up" to an old battery?

I'm confused by your description of the corrosion as "black". Usually "corrosion" of the cable where it attaches to the battery is white, which is the color of lead sulfate. It occurs because the sulfuric acid in the battery leaks/splashes/vents out to the top and reacts with the lead fitting on the end of the cable.

I have no idea what would cause black corrosion on lead.

Er... yes, now that I think about it, it isn't so much corrosion as it is just a black build-up.

I'd like to know what's causing it, and if replacing the battery will rectify it.