Large amounts of sugar are toxic to most everything, so if enough was applied it probably would kill nutgrass and eveything else around there. Like us ants are attracted to anything sweet so applying sugar to your soil would attract them. Dawn detergent is made from non renewable resources so it is something I do not use and would not use on my organic yard anywhere.
Yellow nutsedge, like all sedges, prefers to grow in soils that are too moist, although they have adapted to many soil types. The simplest control I have found is to not water so much.

Here is a link that might be useful: Yellow nutsedge

As kimmsr [almost] said, nutgrass is a swamp grass. I've been discussing this topic with a guy in Phoenix who sprayed molasses and shampoo in the areas where he had nutgrass in his bermuda lawn. What happened was the places where the soil used to hold standing water no longer do that. Those were the nutgrass areas. He just reported to me today that his nutgrass is almost gone in the back. I could not say whether it was due to the molasses or the shampoo but I can say that the result of opening up the soil is what really fixed the problem. With proper drainage, nutgrass has a hard time getting going.

I have patches of nutgrass in my vegetable garden. most of the nutgrass is in the bean roes. My question is if i spray the nutgrass with sugar water or molassis will that kill the bean plants?

I've nost seen a sugar water solution kill Yellow Nut Sedge, yet because it is quite tough, but that sugar water solution could kill, or seriously harm, your bean plants.

I would not think the sugar or molasses would have any affect on the bean plants. In fact I would expect to see an improvement in health of the plants. There is a group of cotton farmers in the Texas Panhandle that all they do is spray molasses at 1 gallon per acre, 4x per season. Beans might be different, though.

Do you have standing water at any time in your bean rows? How long has this area been a garden and do you till it every year?