If log64x2+log8y+3log512(yz)=4\log_{64}{x^{2}+\log_{8}{\sqrt{y}+3\log_{512}{(\sqrt{y}z)}}}=4log64x2+log8y+3log512(yz)=4, where x,y and z are positive real numbers, then the minimum possible value of (x+y+z)(x+y+z)(x+y+z) is
48
36
24
96