МЧ
Мария Чиркова
n=1: 1^3=1^2
n=k: 1^3+2^3+...+k^3=(1+2+...+k)^2
n=k+1: 1^3+2^3+...+k^3+(k+1)^3=(1+2+..+k+(k+1))^2=((k+2)(k+1)/2)^2
1^3+2^3+...+k^3+(k+1)^3=(1+2+...+k)^2+(k+1)^3=(k(k+1)/2)^2+(k+1)^3=(k+1)^2(k^2/4+(k+1))=((k+1)(k+2))^2/4