<Dl> <Dd> ∑ i = 0 n i 3 = (∑ i = 0 n i) 2 (\ displaystyle \ sum _ (i = 0) ^ (n) i ^ (3) = \ left (\ sum _ (i = 0) ^ (n) i \ right) ^ (2)) </Dd> </Dl> <Dd> ∑ i = 0 n i 3 = (∑ i = 0 n i) 2 (\ displaystyle \ sum _ (i = 0) ^ (n) i ^ (3) = \ left (\ sum _ (i = 0) ^ (n) i \ right) ^ (2)) </Dd> <P> generalized to begin a series at any natural number value (i.e., m ∈ N (\ displaystyle m \ in \ mathbb (N))): </P> <Dl> <Dd> (∑ i = m n i) 2 = ∑ i = m n (i 3 − i m (m − 1)) (\ displaystyle \ left (\ sum _ (i = m) ^ (n) i \ right) ^ (2) = \ sum _ (i = m) ^ (n) (i ^ (3) - im (m - 1))) </Dd> </Dl>

Sum from 1 to n of a constant