Naive Approach

The naive approach to all-pairs shortest paths is to run Dijkstra from every vertex. If you run Dijkstra $n$ times, the total time is $O(n^2 \log n + nm)$. For dense graphs where $m \approx n^2$, this becomes $O(n^3 \log n)$.

Floyd-Warshall gives you $O(n^3)$ with no logarithmic factor and much simpler code. It also works with negative edges. The code is about $10$ lines compared to Dijkstra's priority queue machinery.

Space complexity is $O(n^2)$ for the data structures used.