(lg8+lg1000)lg5+3(lg2)^2+lg6^-1+lg0.006
=(3lg2+3)lg5+3(lg2)^2-lg6+lg6-3
=3lg2lg5+3lg5+3(lg2)^2-3
=3lg2(lg5+lg2)+3lg5-3
=3lg2+3lg5-3
=3-3
=0