Evaluate $\displaystyle \int\int_{{S}}{x}^{{2}}+{y}^{{2}}-{z}\ {d}{S}$ where $\displaystyle {S}$ is the part of the cone $\displaystyle {z}^{{2}}={x}^{{2}}+{y}^{{2}}$ that lies between the planes z = 2 and z = 6.