Alistair of Histon and Impington Infants School sent us a very clearly explained solution to this problem:

Fred did not cut his into four pieces, because it is the same as Charlie and David's only cut again, which means that he had eight pieces.
I have spotted that David and Charlie both cut their cubes into cuboids.
The six cubes shown were cut by:
David, Belinda, Andy,
Ellie, Charlie, and Gill

Thank you Alistair!