Weighted sum of the sixth powers of Horadam numbers

Ohtsuka and Nakamura found simple formulas for $\sum_{j=1}^n{F_j^6}$ and $\sum_{j=1}^n{L_j^6},$ where $F_k$ and $L_k$ are the $k$-th Fibonacci and Lucas numbers, respectively. In this note we extend their results to a general second order sequence by deriving a formula for $\sum_{j=1}^n{(-1/q^3)^jw_{j + t}^6},$ where $(w_j(w_0,w_1;p,q))$ is the Horadam sequence defined by $w_0,\,w_1;\,w_j = pw_{j - 1} - qw_{j - 2}\, (j \ge 2);$ where $t$ is an arbitrary integer and $w_0,$ $w_1,$ $p$ and $q$ are arbitrary complex numbers, with $p\ne 0$ and $q\ne 0.$ As a by-product we establish a divisibility property for the generalized Fibonacci sequence.