MathNet 2014 Question 36

Let $a$, $k$ be positive integers and let $n$ be a nonnegative integer. Show that $(ka^2 + 1)^{2n+1}$ can be expressed as a sum of $k + 1$ squares and $(ka^2 + 1)^{2n+2}$ can be expressed as a sum of $(k + 1)^2$ squares.