(x+y+z)^3 - x^3 - y^3 - z^3
\(=x^3+y^3+z^3+3xy\left(x+y\right)+3yz\left(y+z\right)+3xz\left(x+z\right)-x^3-y^3-z^3\)
\(=3x^2y+3xy^2+3y^2z+3yz^2+3x^2z+3xz^2\)
\(=3\left(x^2y+xy^2+y^2z+yz^2+x^2z+xz^2\right)\)
3.(2^2 +1 ).(2^4 +1).(2^8 +1).(2^16 +1)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^{16}-1\right)\left(2^{16}+1\right)=2^{32}-1\)