The cuboid an be cut along the length and breadth face in pieces. so each piece has length of 7 unit and breadth 6 unit and hight of 1 unit. Let us call these pieces of type A.
There will be 9 number of pieces of A type. So the pieces are of 7 x 6 x 1 unit demension. Now this type of one piece having volume is 7 x 6 x 1 unit = 42 unit.

Then we cut each piece of type A along length in pieces. So each piece has length of 1 unit and breadth of 6 unit and hight of 1 unit.
Let us call these pieces of type B. There will be 7 number of pieces of B type from each of A type pieces.
So the pieces are of 1 x 6 x 1 unit demension. Now this type of one piece having volume is 1 x 6 x 1 unit = 6 unit.

Then we cut each piece of type B along breadth in pieces. So each resultant piece has length of 1 unit and breadth of 1 unit and hight of 1 unit.
Let us call these type of pieces of type C. There will be 6 number of pieces of C type from each of B type pieces.
So the pieces are of 1 x 1 x 1 unit demension. Now this type of one piece having volume is 1 x 1 x 1 unit = 1 unit.

Now we have total number of unit pieces 7 x 6 x 9.
The total unit volume occupied pieces in a full cuboid is 7 x 6 x 9.
So the total volume occupied = 378 unit.