The big question is whether or not they have all of their outer feathers grown in yet, because if they don't, they should still be in a Brooder, kept at an ambient temperature of around 80 degrees F or so. If they are on the bottom of their weaning-cage without all of their feathers, they will be too cold to properly digest their formula, and will develop yeast infections in their crops.
Also, are you making sure that all of the formula you are feeding them is always between 104 degrees F and 110 degrees F? You must use a candy/cooking thermometer and make sure that the formula you are feeding them is always between those two temps, one degree cooler and they will develop fungal infections in their crops and not be able to properly digest their formula, and one degree higher and they will develop crop burns, which will become infected and usually require surgery to repair...So you must always have the candy thermometer in the formula...
And as SilverSage said, you surely are feeding them a baby bird hand-feeding formula, right? Such as Kaytee, Roudybush, etc.? Because if you're feeding them anything else, such as "porridge", oatmeal, baby cereal, etc., they will either become severely malnourished and not survive due to vitamin/mineral/nutritional deficiency, or they will die of Iron-Poisoning, as birds cannot process Iron, and their foods are specially formulated with very low Iron content, specifically the baby-bird hand-feeding formulas, they contain very little to no Iron because they are so sensitive to it. On opposite spectrum, ALL human baby foods/cereals contain extra Iron, they are fortified with it, and it's extremely common for people to try to hand-feed baby birds human baby cereals, such as Cerelac or any of the human baby rice-cereals, and they end up killing the baby birds very quickly due to Iron poisoning.
I'm going to assume that at 6 weeks old they probably do not have all of their outer feathers, and the reason they are still "huddling" in the corner of the bottom of the cage is because they are too cold. You need to at the very least get a heating pad with an adjustable temperature underneath the cage, and then cover 3 sides of the cage with a big towel or blanket, so that the heat will stay inside the cage. Leave the front of the cage uncovered so that they get light and so that you can see them...ideally you'd have them in a Brooder, but at 6 weeks old they may be old enough to survive in a weaning-cage as long as you have an external heat source.
Also, please be sure that you have properly read-up on hand-feeding technique, as you can easily aspirate the formula into their lungs and kill them. And you also need to get a digital kitchen scale so that you can weigh them each day, first thing in the morning before you feed them their first hand-feeding, so that you can make sure that they're gaining up until the point that they fledge, which should be soon, around 7-8 weeks old.
Again, if you're not feeding them a real baby bird hand-feeding formula that you bought from the pet store, then you need to go and buy some immediately, as there are really no replacements or substitutes for it, there is no other way for them to get the nutrition they need, and they'll not survive otherwise.
And please also make sure that you have their weaning-cage set up with lots of different types of toys, different food and water dishes/containers, ladders, swings, etc., as this is the time that they should be starting to learn how to play, eat out of different containers, etc. If they don't have all of these things inside of their weaning cage, they will not properly learn, and they can end-up with some serious behavioral issues.
Please don't ever bring home a baby bird from a breeder that is not fully-weaned!!! There are so many ways that you can kill them, make them seriously ill, and cause them neurological issues when you don't know what you're doing, and the breeder that sold these birds to you is a totally irresponsible and unscrupulous breeder who knew better than to send those babies home with you...They know very well that unweaned babies who go to inexperienced homes typically die due to improper ambient/housing temperatures, improper formula temperatures (usually the formula is far too cold for the babies and they die of a yeast infections and/or crop-stasis), and from aspiration of formula into the lungs...