7/8

2x+2/x=3 x^3+1/x^3+2=y

2x+2/x=3==>x+1/x=3/2------- (1) (x+1/x)^3=27/8------------------(2) (x+1/x)^3=x^3+1/x^3+3x+3/x=(y-2)+3*(x+1/x), considering (1) & (2), we get 27/8= y-2 +3*3/2==> y=27/8-5/2=7/8 x^3+1/x^3+2=7/8