Using odd numbers for squares/cubes

Here are ways for obtaining squares/cubes using odd numbers-
Consider the following set of odd numbers-
1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37etc
For getting squares you simply add them consecutively-
1=1*1
1+3=4=2*2
1+3+5=9=3*3
1+3+5+7=16=4*4etc
1+3+5+.......37=361=19*19 and further squares.
For getting cubes you add as follows-
1=cube of 1
3+5=8=cube of 2
7+9+11=27=cube of 3
13+15+17+19=64=cube of 4
21+23+25+27+29=125=cube of 5 etc
Considering  the above groups as the 1st,2nd,3rd,4th &5th, the 'n'th group will be as follows-
First term n^2-n+1
Last term n^2+n-1
No of terms-n
Sum of all the terms=n*average of the first &last term=n*n^2=n^3=cube of n
For example the 30th group will have 871 as the first term,929 as the last term and the sum of
all the terms will thus be 30*(871+929)/2=30*900=27000=cube of 30