Subtraction Triangle for n-th powered number series

From the above triangle, the top row represent number series to the 2nd power of increment integers: $1^2, 2^2, 3^2, 4^2$ and so on. Second row of numbers is then built by finding the differences between the numbers row above, and this process is repeated. It is noticed that the rows will eventually end with final row to be 0.

This similar triangle can be built even if you raise the power of $n$ , and all of these triangles will end up with final row of 0.

For example, for the power of 3 on increment integers: $1^3, 2^3, 3^3, 4^3...$ as shown below: Assuming the integer above the final row of 0 to be $T$ , and the power raised to be $n$ , which of the following statement is true?