Question 789073
We have to assume that the cube is dense enough so it will not float, because if it floated we would need to now what fraction of the cube was submerged.
 
Since the original depth of water, 9 cm, was higher than the height (8 cm) of the cube, the entire cube will be underwater, displacing a volume of water equal to the volume of the cube.
The volume of the cube is
{{{(8cm)^3=512}}}{{{cm^3}}}
The water displaced will fill a cylinder of radius 7 cm and height {{{h}}}{{{cm}}}  above the previous water level.
The volume of the cylinder of displaced water is
{{{pi*(7cm)^2*h=512}}}{{{cm^3}}}
{{{h}}}={{{512/(pi*(7cm)^2)}}}={{{512/49pi}}}{{{cm=3.3cm}}}(rounded to the nearest millimeter).