If the cuboid is not blocking ,

Number of cubes that can be fit lengthwise = 24cm ÷ 3cm = 8

Number of cubes which can be fit breadthwise = 18cm ÷ 3cm = 6

Number of cubes in 1 layer
= 8 x 6
= 48

Now in the centre of a layer, there are 4 cubes. The combined base area is that of a 6cm x 6cm square.

But since the cuboid is there, and it is in the exact centre, it blocks a base area of 4cm x 4cm. This is within the centre of that 6cm x 6cm square.

Since it partially blocks that space, that means that you can't fit that 4 cubes in the centre.

So number of cubes in 1 layer
= 48 - 4
= 44

Number of layers
= Number of cubes which can be fit heightwise = 9cm ÷ 3cm = 3

Now the cuboid is 9cm tall (same as the box) , every layer has the centre blocked.

So max number of cubes

= 3 x 44
= 132

How to get the 6cm x 6 cm square?

Is 4 cubes space with 3cm each. Total length 3+3=6cm in the centre.
⬛⬛
⬛⬛

Got it. Thanks!

Nice use of the square!