The minimum number of cubes to cover every visible face on a cuboid measuring $3\times 2\times 1$ is twenty-two.

If we then add a second layer to this solid it would require forty-six cubes to cover every visible face, the third layer would require seventy-eight cubes, and the fourth layer would require one-hundred and eighteen cubes to cover every visible face.

However, the first layer on a cuboid measuring $5\times 1\times 1$ also requires twenty-two cubes; similarly the first layer on cuboids measuring $5\times 3\times 1$, $7\times 2\times 1$, and $11\times 1\times 1$ all contain forty-six cubes.

We shall define $C(n)$ to represent the number of cuboids that contain $n$ cubes in one of its layers. So $C(22)=2$, $C(46)=4$, $C(78)=5$, and $C(118)=8$.

It turns out that $154$ is the least value of $n$ for which $C(n)=10$.

Find the least value of $n$ for which $C(n)=1000$.