I figured it wouldn't be too long before the Kallax was mentioned
I thought about using that at one point too - the price is certainly right. But as @audphile1 said, it needs to be reinforced as it's not very stable on its own. Not surprisingly at its price, it's made out of cheap materials and I really didn't think it would stand up to the weight of my record collection. But lots of people swear by it and there's many videos online that describe how to reinforce it, so it might be worth a try.
Oh, and given the interior dimensions of the cubes (13.25"), I'd guess they'd store somewhere between 75 and 100 records, but someone here who is actually using it should have a more accurate estimate.

