[?] Create an iterating function - from the following required form?

Questions
1

Hi All,

I am trying to create an iterating function - from the following data in the required form?
Below I have shown the ‘structure’ of the function & the correct output values for each element in the output list.
Ideally I trying to code Nest or NestList or some other function to give me the correct function to produce the desired output results.
But I am not sure how to set this up.

Please could someone review the following & provide suggestions for coding such a function.

{(360*30^2*(4)),
 (360*30^2*(4)) + (360*30^2*(16)),
 (360*30^2*(4)) + (360*30^2*(16)) + (360*30^2*(36)),
 (360*30^2*(4)) + (360*30^2*(16)) + (360*30^2*(36)) + (360*30^2*(64)),
 (360*30^2*(4)) + (360*30^2*(16)) + (360*30^2*(36)) + (360*30^2*(64)) \
+ (360*30^2*(100)),
 (360*30^2*(4)) + (360*30^2*(16)) + (360*30^2*(36)) + (360*30^2*(64)) \
+ (360*30^2*(100)) + (360*30^2*(144)),
 (360*30^2*(4)) + (360*30^2*(16)) + (360*30^2*(36)) + (360*30^2*(64)) \
+ (360*30^2*(100)) + (360*30^2*(144)) + (360*30^2*(196)),
 (360*30^2*(4)) + (360*30^2*(16)) + (360*30^2*(36)) + (360*30^2*(64)) \
+ (360*30^2*(100)) + (360*30^2*(144)) + (360*30^2*(196)) + \
(360*30^2*(256)) }

Output = {1296000, 6480000, 18144000, 38880000, 71280000, 117936000, \
181440000, 264384000}

Many thanks for your help & attention.
Best regards,
Lea…

2

You can try with FindSequenceFunction. The output is

216000 (n + 3 n^2 + 2 n^3)
3

Hi Gianluca ,
That’s a great answer - more simple than expected.
Many thanks for your help.
Best regards, Lea…