I bet its birds, not sure humans would be ready to carry that amount of eggs unless they knew they were left there and they had some way of carrying them!! It would be great to catch on camera, birds comming in and out taking eggs away for thier breakfast!!!! funny but it would make me angry too. I used to watch squirrels take the tomatoes out of a neighbours green house, seeing them run up the tree with on in thier mouths was funny.
Hope you catch the culprit! check around high spots for egg shells!