We extend results of Jagy and Kaplansky and the present authors and show that for all k ≥ 3 there are infinitely many positive integers n, which cannot be written as x2 + y2 + zk = n for positive integers x, y, z, where for k≢0mod4k≢0mod4 a congruence condition is imposed on z. These examples are of interest as there is no congruence obstruction itself for the representation of these n. This way we provide a new family of counterexamples to the Hasse principle or strong approximation.