  The Matrix Waring problem is if we can write every matrix as a sum of $k$-th
powers. Here, we look at the same problem for triangular matrix algebra
$T_n(\mathbb{F}_q)$ consisting of upper triangular matrices over a finite
field. We prove that for all integers $k, n \geq 1$, there exists a constant
$\mathcal C(k, n)$, such that for all $q> \mathcal C(k,n)$, every matrix in
$T_n(\mathbb{F}_q)$ is a sum of three $k$-th powers. Moreover, if $-1$ is
$k$-th power in $\mathbb{F}_q$, then for all $q>\mathcal C(k,n)$, every matrix
in $T_n(\mathbb{F}_q)$ is a sum of two $k$-th powers. We make use of Lang-Weil
estimates about the number of solutions of equations over finite fields to
achieve the desired results.
