First, 6x resistance= 1/8 damage
Now lets find the abilities that give a resistance to a type: Thick Fat and Heatproof.
Now we need to find a Pokémon with this ability and that already has a 1/4 resistance to a type.
We can start with Thick Fat.
Dewgong has a 1/4 resistance to ice. Add in Thick Fat, and it becomes 1/8.
Same with Spheal, Sealeo and Walrein.
For Heatproof, only two Pokémon can have it and they don't get a 1/4 resistance in the first place.
No Pokémon can be 1/8 resistant without an ability, because no Pokémon can have a 1/4 resistance from only one type.
Source: Experience, here, here, here and here.