Simple cubic (or primitive cubic):
The atoms in the corners are shared between 8 other unit cells, so they are regarded as 1/8th of an atom. This unit cell therefore has 8 x (1/8) atoms, or 1 in atom in total.
Body-centered cubic:
This has a a single atom inside the cube, so the unit cell contains a total of two atoms.
Face-centered cubic:
This has an atom on each face shared between two unit cells. So in total it contains (8 x (1/8)) + (6 x (1/2)), or 4 atoms in total.
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