Given: \( \Large a+b+c=0 \)

=> \( \Large a+b = -c \)

Taking cube on both sides, we have

\( \Large \left(a+b\right)^{3} = \left(-c\right)^{3} \)

=> \( \Large a^{3}+b^{3}+3ab \left(a+b\right)=-c^{3} \)

=> \( \Large a^{3}+b^{3}+3ab \left(-c\right)=-c^{3} \)

=> \( \Large a^{3}+b^{3}+c^{3}=3abc \)