It doesn't taste weird, but I don't know why this happened. I have never used this unenamelled pot to make soup.
Does making chicken stock in a cast iron dutch oven turn the liquid black?
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When did the stock turn black? While it was cooking or after?
There are only a couple reasons why the stock turned black.
1) The pot was not sufficiently seasoned before use.
2) the stock was left in the iron pot too long.
If the pot was new, its almost certain the pot came with a protective coating that must be removed before use. If the coating was not removed, then it is possible that caused the stock to turn black. However, I tend to favor the theory that that pot was not properly seasoned before use. If it was the coating, then, chances are the stock would've tasted weird, like a chemically taste perhaps. No worries. Give the pot a good scrubbing with some steel wool, mild soap and water as hot as you can stand it. Then apply a light coat of oil, preferably something that will not turn rancid after a couple days. I like to use coconut oil because it resists turning rancid well.
The black discoloration was likely iron that leached out of the pot into the stock which typically happens with a pot that has not been properly seasoned before use. Its not toxic. After all its iron. But, I would not recommend using the stock for obvious reasons.
After each use, wash with mild soap and water and dry thoroughly. As I said, give the pan a light coat of oil and store in a dry place with the lid off. The more cast iron is used and oiled, the better it gets in terms of non-stick properties.
Never store food in cast iron. It can take on a metallic taste, cause the food to turn black and/or or cause the iron to rust.
I hope this helps.
As noted, if your seasoning wasn't that good, you can get some coloring. Also, long cooking of liquids does break down even well seasoned pots to a degree. It's really not the right choice for making a stock.