A non-isotropic solid metal cube has coefficients of linear expansion as: $5 \times 10 ^ { - 5 } / { } ^ { \circ } \mathrm { C }$ along the x-axis and $5 \times 10 ^ { - 6 } / { } ^ { \circ } \mathrm { C }$ along the y and the z-axis. If the coefficient of volume expansion of the solid is $\mathrm { C } \times 10 ^ { - 6 } / { } ^ { \circ } \mathrm { C }$ then the value of $\mathbf { C }$ is $\_\_\_\_$