Gray Mold Or Damping Off

This is a fungal problem, and there are several possibilities. The two most common are Botrytis and one of the fungi that cause “damping off.” The first is gray mold (Botrytis), which usually takes new seedlings a leaf at a time. It is most active in cool, humid environments, so you can counteract it by warming the temperature, reducing humidity (which warming alone will do), and increasing air circulation. There are also fungicides made to treat infected plants. The second possibility is damping off disease, which includes a complex of fungi that kill the seedling by attacking its stem. The up-front prevention is to use absolutely sterile soil mix, with no reused soil from last year or garden compost. The cubes like you’ve used might be keeping the area far too wet. Once damping off starts, you can’t stop it. Good air circulation will help in the future as well – a fan on a timer that blows the seedlings helps strengthen them and keep the air circulating.