How this calculation works
The identity uses the square of the entire triangular sum. It does not square each addend separately.
THE FORMULA
[n(n+1)/2]²A worked example
For n = 10, the triangular number is 55, and 55² = 3,025.
Good to know
An empty sum is zero.
Reference: NIST DLMF, Functions of Number Theory (opens in a new tab) ↗
Read the result
Evaluate a finite cube sum using the square of its triangular number.
The primary result is labeled “Sum of cubes”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
An empty sum is zero.
For a related exercise, try the greatest common divisor.
A few questions, answered
How can I check the default inputs by hand?
For n = 10, the triangular number is 55, and 55² = 3,025.
Which rule does this calculator apply?
[n(n+1)/2]²