  A new family of generalized Pell numbers was recently introduced and studied
by Br\'od \cite{Dorota}. These number possess, as Fibonacci numbers, a Binet
formula. Using this, partial sums of arbitrary powers of generalized Pell
numbers can be summed explicitly. For this, as a first step, a power $P_n^l$ is
expressed as a linear combination of $P_{mn}$.
  The summation of such expressions is then manageable using generating
functions. Since the new family contains a parameter $R=2^r$, the relevant
manipulations are quite involved, and computer algebra produced huge
expressions that where not trivial to handle at times.
