Nim Square

Alice and Bob play the game Nim Square.

Nim Square is just like ordinary three-heap normal play Nim, but the players may only remove a square number of stones from a heap.

The number of stones in the three heaps is represented by the ordered triple $(a,b,c)$.

If $0≤a≤b≤c≤29$ then the number of losing positions for the next player is $1160$.

Find the number of losing positions for the next player if $0≤a≤b≤c≤100\ 000$.