m^2-m-1=0,n^2-n-1=0
m,n是方程x^2-x-1=0的两个根
m+n=1,mn=-1
m^3+n^3-2m^2-2n^2+2008
=(m+n)(m^2-mn+n^2)-2(m^2+n^2)+2008
=m^2+1+n^2-2m^2-2n^2+2008
=-(m^2+n^2)+2009
=-(m^2+n^2+2mn)+2009+2mn
=-(m+n)^2+2009-2
=-1+2009-2
=2006