In part it reads like you're talking about one Pack but you say "...
groups (of 15 or so) ..." but don't say whether it's one Pack or a multi-pack group or a combined groups/District/County/Regional/or type camp (and you could be an A.D.C Cubs

), so ...
How many Cubs in total?
Are they all known to you and you to them?
Are there any SEN needs?
Any with food sensitivities/intolerance(s)/allergies?
How many leaders?
What's your (expected) ratio on the base(s)?
Can you take materials in? (Thinking natural shelters here ~ we often get them to make mini versions of proper shelters for glove puppets

)
Is the site looking to drop a tree or two that you could use? (Site maintenance stuff) If there is then perhaps give/organise a short talk covering the importance of site maintenance, conservation, things which might rely on the living tree, what lives on dead trees ... and get them to help tidy up* the felling(s) ~ if you can tie it all together it should fit in nicely with the 'Camp Site Service' badge bits without the Cubs even realising that they're working
* Tidying up = move the brash to make natural shelter(s) and then being responsible by breaking the shelter(s) down ('leave no trace'

) and stacking it all in a place agreed with the site for it to be used as an insect habitat ... mini beast hotel

. As already mentioned, this tidying would also count toward Site Service
Art in the park?
Gods Eyes?
Bamboo pioneering? (elastic bands inplace of 'proper' lashings ~ the idea being to get Cubs to understand how to construct strong structures without having to teach them the knots and lashings on the base and/or fixate on trying to get knots and lashings good and tight on what might be their first attempt

).
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The problem with doing food is opting for one which can't easily go wrong ~ there's a huge difference between undercooking a damper twist and undercooking a sausage

. How are you going to monitor the status of the food? How many cubs would you have around a fire ~ certainly not a group of 15 cooking individual items :yikes: How would you keep on top of controlling the fire and its 'needs'?
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Accepting that Cubs and Beavers are different wee beasties ...
Last weekend I helped with a Beaver activity base ~ over 300 Beavers went through each area. One part of our area was cooking on an open fire ~ can you imagine trying to keep >300 beavers safe around a cooking fire and makiing sure that what they'd cooked was safe to consume? :yikes: . We opted to have them work as teams of four to make their own dish which was then cooked by an adult who talked to them about various things like fire safety, food hygiene ... and even why hot air rises and 'floating' tin foil to draw a comparisson to hot air balloons and how they stay in the sky

.
We also had other activities available which required low levels of supervision ~ which freed up time to deal with and space around, the cooking fire

(We had two adult leaders plus an Explorer Young Leader running a base of seven different activities ~ because we made use of the leaders acompanying each Beaver Colony/Lodge

)