Generalize the following sequence of identities and prove yo

Generalize the following sequence of identities and prove your generalization. 1=1, 3+5=8, 7+9+11=27, 13+15+17+19=64

Solution

these are all real odd numbers starting from 1:

1, 3, 5, 7, 9, 11, 13 ........

the first cubed of 1 : 1 = 1^3 = 1
the next cubed of 1 : 3 + 5 = 2^3 = 8
the next cubed of 1 : 7 + 9 + 11 = 3^3 = 27

and so on all the way to infinity!!