OIMU 1998 Problem 3

The positive divisors of a positive integer $n$ are written in increasing order starting with 1. $$1=d_1<d_2<d_3<\cdots<n$$ Find $n$ if it is known that:i. $n=d_{13}+d_{14}+d_{15}$ ii. $\,(d_5+1)^3=d_{15}+1$