Was it ripe? Hubbard squash usually don't ripen until later in the year. I doubt it was, a newbie would likely not know the difference. An unripe Hubbard can be eaten, but it won't last very long off the vine without rotting. Especially if the stem was broken off. How long was it off the vine?
Hubbards, and other winter squash, are known for their ability to keep for long periods of time in storage. But to do so they have to be completely ripe, the stem must be intact, and there can be no cuts or injuries. Some people go as far as to wipe their winter squashes down with disinfectant before storing.

Thanks for the info. Is there a big difference in flavor when they're ripe? I got another one about a month ago and it was quite tasty. It was the first time I had tried hubbard squash. The one with the mold looked about the same as that one. I'm not sure how long it had been off the vine, a couple of weeks, I guess. The person who planted them had a huge garden and put some winter squash in as an afterthought. If he plants them again, I'll let him know not to harvest them too soon.

I've never tasted one that wasn't ripe. One crude test of ripeness is to press your thumbnail into the shell. You shouldn't be able to penetrate a ripe winter squash this way. Sometimes opening a ripe Hubbard Squash requires a hatchet or power tools. Not kidding, they have freaking tough shells.