Sum square difference
Jelly, &nbsp;5&nbsp; 4 bytes

Ḋ²ḋṖ


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Implements  \$\sum_{i=2}^n{(i^2(i-1))}\$...

Ḋ²ḋṖ - Link: non-negative integer, n
Ḋ    - dequeue (implicit range)       [2,3,4,5,...,n]
 ²   - square (vectorises)            [4,9,16,25,...,n*n]
   Ṗ - pop (implicit range)           [1,2,3,4,...,n-1]
  ḋ  - dot product                    4*1+9*2+16*3+25*4+...+n*n*(n-1)