Question 808851
If I say that {{{ x }}} is the number of cubes
along an edge including the corners, then
{{{ x - 2 }}} is the number not including 
the corners.
Going around the cube I have {{{ 12 }}}
edges and {{{ 8 }}} corners, so
{{{ 12*( x - 2 ) + 8 = 80 }}}
{{{ 12x - 24 + 8 = 80 }}}
{{{ 12x = 80 + 16 }}}
{{{ 12x = 96 }}}
{{{ x = 8 }}}
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The number of unit cubes should be
{{{ 8^3 = 512 }}}
512 unit cubes