Question

Without actually calculating the cubes, find value of (1)^3+(2)^3+2(4)^3+(-5)^3+(-6)^3

Answer 1

$1^{3}+2^{3}+2.4^{3}+(-5)^{3}+(-6)^{3}=1^{3}+2^{3}+4^{3}+4^{3}+(-5)^{3}+(-6)^{3}$
=$[1^{3}+4^{3}+(-5)^{3}]+[2^{3}+4^{3}+(-6)^{3}]=3[1.4.(-5)]+3[2.4.(-6)]$
=-60-144=-204
If a+b+c=0, then $a^{3}+b^{3}+c^{3}$=3abc