the spheres in the bcc structure are in contact along the body diagonal of the cubic unit cell, but they are not in contact along the edges of the unit cell.

This is not a close packed structure

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Each atom on the vertex of the cubic unit cell contributes 1/8 (it is shared between 8 unit cells) so the total number of atoms in the unit cell is

8x(1/8) + 1 = 2