Confusion about bound surface current of a cube

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SUMMARY

The discussion clarifies that when the magnetization vector of a cube is oriented in the z direction, the bound surface current is not always zero. While the z-component does not contribute to the current due to the cross product being zero, bound surface currents do exist on the X-Y outer surfaces of the cube. These currents circulate around the cube, analogous to the surface currents found on a circular rod.

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If the magnetization vector is in the z direction, is the bound surface current of a cube always 0, since z cross z is 0, and x and -x cancels and y and -y cancels out?
 
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There will be bound surface currents on the X-Y outer surfaces that circulate around the cube.
This is just like the surface currents on a circular rod. The shape is just different.
 

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