>>664
n = 1のとき成り立つ。
n = m のとき成り立つとすれば
Σ_{k=1 to m} k^3 = {m(m+1)/2}^2
Σ_{k=1 to (m+1)} k^3 = {m(m+1)/2}^2 + (m+1)^3 = (1/4) (m+1)^2 { m^2 + 4(m+1)}
= (1/4) (m+1)^2 (m+2)^2 = {(m+1)(m+2)/2}^2
となり n = m+1のときも成り立つ。