I was wondering if the tunnels under Gringotts were dug out by magic like by the goblins or some form of magic; or did nature make them? Any theories?
London is famous for having almost as much construction under the ground as above it; even entire rivers have been paved over and moved underground in the city.
While the design in the films suggested that the tunnels were natural caves, this is highly unlikely given the geology of the city; there is no limestone or other cave-forming rock beneath London. On the other hand, there is a fairly extensive tradition of goblins being tunnelers in English folklore, and especially in modern fantasy (see Tolkien's goblins).
Gringotts underground tunnels are building on long-established folklore and traditions, both of tunnels beneath London and of goblins as underground creatures. While there's no absolute canonical answer (that I'm aware of, at least), it does seem likely that the tunnels were dug by the goblins specifically to store treasure.