So, first, we have to calculate the volume of the cube and then the volume of the cylinder. Then, the remaining volume will be the Volume of the cube minus the volume of the latter.
[tex]\begin{gathered} Vcube\text{ = }l\text{ x }l\text{ x }l \\ Vcube\text{ = 6in x 6in x 6in = 216 in}^3 \\ \\ Vcylinder\text{ = }\pi r^2h \\ =\text{ }\pi\text{ \lparen2in\rparen}^2\text{ \lparen6in\rparen} \\ =\text{ 75.36 in}^3 \\ \\ RemainingVolume=\text{ }216in^3\text{ - }75.36in^3^ \\ \\ =\text{ }140.64\text{ in}^3\text{ }\approx\text{ 141 in}^3 \end{gathered}[/tex]