Pyramidal Six

The centroid of the cuboid is also the midpoint of the axes between the faces' centers, so the height of the pyramid will be half of either width, length, or height of the cuboid, depending on their base orientation.

For instance, if the cuboid has the green base, with width $w$ and length $l$ , and height $h$ , the pyramid with the green base will have the volume of $\dfrac{1}{3}\times w\times l\times \dfrac{h}{2} = \dfrac{wlh}{6}$ or equal to one-sixth of the cuboid's volume.

Similarly, for the pink-based pyramid, the volume = $\dfrac{1}{3}\times w\times h\times \dfrac{l}{2} = \dfrac{wlh}{6}$ .

And finally, for the orange-based pyramid, the volume = $\dfrac{1}{3}\times h\times l\times \dfrac{w}{2} = \dfrac{wlh}{6}$ .

Therefore, all the six pyramids have the same volume.

We know the volume of any solid is : Area of the base × it's height. All these pyramids are going to have the same area of the base since the bases are all congruent squares. Also, since all these pyramids have the same vertex which is the centroid of the cube, then all their heights are going to be congruent. Thus, the six pyramids have the same volume. (under the assumption the faces are all squares).