Question

Prove by induction that n in set positive

1**3 + 2**3 + 4**3 ... n**3 = n**2(n+1)**2/4

base case n = 1

n**(n+1)**2/4

1**2(1+1)**2/4

1(2)**2/4

4/4 = 1 so true

inductive step n=k

n=k+1

1**3 + 2**3 + 4**3 ... k**3 = k**2(k+1)**2/4

k**2(k+1)**2/4 + (k+1)**3 = (k+1)**2 (k+1+1)**2/4

k**2(4+1)**2/4+ 4(k+1)**3/4 = (k**2+1)(k+2)**2/4

Am i on the right track ?