We say that a number $n \ge 2$ has the property $(P)$ if, in its prime factorization, at least one of the factors has an exponent $3$. a) Determine the smallest number $N$ with the property that, no matter how we choose $N$ consecutive natural numbers, at least one of them has the property $(P).$ b) Determine the smallest $15$ consecutive numbers $a_1, a_2, \ldots, a_{15}$ that do not have the property $(P),$ such that the sum of the numbers $5 a_1, 5 a_2, \ldots, 5 a_{15}$ is a number with the property $(P).$