Calculate the third and fourth nearest neighbours in bcc
With $\sqrt3\over2$ being that close to $1$, BCC packing is better not looked at in terms of coordination spheres. But if you insist...

Say you are sitting in the center of a cell. Then:


Your first neighbours are at the corners of the same cell.
Second neighbours are at the centers of the nearest adjacent cells.
Third neighbours: centers of the next adjacent cells (those which share two corners with your cell).
Fourth neighbours: far corners of the nearest adjacent cells.


On a side note, there are more than just 8 of the latter.