(a+b+c)³
=(a+b+c)×(a+b+c)×(a+b+c)
=(a²+ab+ac+ab+b²+bc+ac+bc+c²)×(a+b+c)
=(a²+b²+c²+2ab+2ac+2bc)×(a+b+c)
=(a³+ab²+ac²+2a²b+2a²c+2abc)+(a²b+b³+bc²+2ab²+2abc+2b²c)+(a²c+b²c+c³+2abc+2ac²+2bc²)
=a³+b³+c³+3ab²+3a²b+3ac²+3a²c+3bc²+3b²c+6abc