Congruence condition on number of non-cyclic subgroups of prime-cube order for odd prime

In terms of universal congruence condition
Let $$p$$ be an odd prime. The collection of non-cyclic groups of order $$p^3$$ is a fact about::collection of groups satisfying a universal congruence condition.

Statement with symbols
Let $$p$$ be an odd prime and $$P$$ be a finite $$p$$-group (i.e., a group of prime power order where the underlying prime is $$p$$) containing a non-cyclic subgroup of order $$p^3$$. Then, the total number of non-cyclic subgroups of order $$p^3$$ in $$P$$ is congruent to $$1$$ modulo $$p$$.