m^2=m+2,
n^2=n+2,m≠n,
∴m,n是x^2-x-2=0的两根,
∴m+n=1,mn=-2,
m^3+2mn+n^3
=(m+n)(m^2-mn+n^2)+2mn
=m^2+mn+n^2
=(m+n)^2-mn
=1+2=3.