Bino

(1+x)^{n}=C_{0} +C_{1}x +C_{2}x^{2}.............C_{n}x^{n}

(y+1)^{n}=C_{0}y^{n}+ C_{1}y^{n-1}+C_{2}y^{n-2}..............C_{n}

(x+y)^{n}=C_{0}x^{n}+C_{1}x^{n-1}y + C_{2}x^{n-2}y^{2}.........C_{n}y^{n}

if we multiply them then each verticle column will be in term of x^{n}y^{n}

therefore coefficient ofx^{n}y^{n}
is
C_{0} ^{3} + C_{1} ^{3} +C_{2} ^{3}........C_{n}^{3}