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In the cube below, $AB = 1$ unit.

What is the volume of the cube, in cubic units?

$ {\cfrac { \sqrt { 2 } }{ 8 } } $

$ {\cfrac { \sqrt { 3 } }{ 9 } } $

$ \cfrac { 1 }{ 9 } $

$ \cfrac { 1 }{ 8 } $

$1$