\(=a^3+b^3+c^3+3\left(a+b\right)\left(ab+ac+bc+c^2\right)\\ =a^3+b^3+c^3+3\left(a+b\right)\left(ab+c\left(a+b\right)+c^2\right)\\ =a^3+b^3+c^3+3ab\left(a+b\right)+3\left(a+b\right)^2c+3\left(a+b\right)c^2\\ =a^3+b^3=c^3+3a^2b+3ab^2+3\left(a+b\right)^2c+3\left(a+b\right)c^2\\ =\left(a+b\right)^3+3\left(a+b\right)^2c+3\left(a+b\right)c^2+c^3\\ =\left(a+b+c\right)^3\)