Sum of Subrectangle Areas

Consider the grid from $(0, 0)$ to $(N, N)$.

Consider every subrectangle whose four corners have integer coordinates, that is, every $[r_1, r_2] \times [c_1, c_2]$ with $0 \le r_1 < r_2 \le N$ and $0 \le c_1 < c_2 \le N$. The area of such a rectangle is $(r_2 - r_1) \times (c_2 - c_1)$. The following pseudocode computes the sum of the areas of all subrectangles.

sum = 0
for r1 = 0 to N-1
  for c1 = 0 to N-1
    for r2 = r1+1 to N
      for c2 = c1+1 to N
        sum = sum + (r2-r1)*(c2-c1)
print(sum)

Given $N$, compute this sum efficiently. The input contains several test cases.

The first line contains the number of test cases $T$. Each of the following $T$ lines contains a single integer $N$ for that test case. $N$ fits in a 64-bit integer with $0 \le N \le 9223372036854775807$.

For each test case, print the sum defined above on its own line. The sum may exceed the range of a 64-bit integer, so print it as an arbitrary precision integer.