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You cannot convert "watts per meter squared", $\rm W/m^2$, to "watts per meter cubed," $\rm W/m^3$. Square meters measure area, cubed meters measure volume; they are quite different. You might as well say, "I have an acre of sod; how tall is it?" The extra factor of length changes things completely.


This is nothing but a choice of units. Let me make that (hopefully) more clear by explaining more about how choosing units in electromagnetism works: Coulomb's Law is $\vec F = k \frac{q_1 q_2}{r^2} \hat{\vec r}$ for the force between two charges $q_1$ and $q_2$. $k$ is different in the various systems of units - essentially, it depends on how the unit of ...

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