∵　(a-2)²+|b+3|+(c-4)²＝0
∴(a-2)²＝0,　|b+3|＝0,(c-4)²＝0
a-2=0,b+3=0,c-4=0
a=2,b=-3,c=4
∴a³+2b²+3c
=2³+2×(-3)²+3×4
=8+18+12
=38