First, it's important to NOT use the ice until you get this problem cleared up.
Second, it sounds very much like you have a mold growing in the machinery or tubing that feeds water into the unit. I don't know anything about the machinery but it is extremely important to clean ALL tubing and surfaces-- OR to replace things like tubing because those are more difficult to clean on the inside.
Call the manufacturer or read the Owner Manual if you have one. You specifically need to know (1) what places or surfaces does the water pass through or over and (2) what parts can be removed, cleaned, and re-inserted.
Many people believe bleach is effective to clean mold. But, bleach just bleaches the color from the mold-- so there's still mold but you can't see it anymore.
Instead, items contaminated with mold should be washed in hot soapy water made with a good dish detergent. You can add bleach to the detergent water, but every item *must* be thoroughly scrubbed inside and out. Buy a baby-bottle brush to push into tubing and use a twisting motion to scrub the inside of every tube. Make sure to use a clean dish cloth to wash the items.
Run hot water through the tubes and let air dry-- do NOT re-insert while damp. Let all parts thoroughly dry - air dry. Then, wipe with a clean dish towel or plain white paper towel -- paper towels with patterns contain dyes which can leave a chemical smell or aftertaste to the ice.
You may need a service repair man / person to thoroughly clean the unit.
*If the unit is highly contaminated, it will be healthier to replace the unit.
Mold can cause all sorts of physical illnesses, and problems with concentration and memory. Mold CAN kill. You may be so used to the smell and taste that you may not notice it in the ice, except for the evidence of colored ice.
I must repeat-- do not use the ice until the unit is thoroughly checked and cleaned.
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