What wire size for 125A Subpanel?
Make sure your subpanel has enough spaces

The #1 mistake sizing subpanels is getting just enough spaces to do the job today.  Then later, they try to add more loads, particularly 240V loads that gobble up 2 spaces each... and they find a full panel. This is made even worse by the allure of "12 spaces/24 circuits" - that second figure has been a complete lie for several years, now that most circuits need AFCI or GFCI breakers, which take a full space.  

"Running out of breaker spaces" should simply never happen, given that extra breaker spaces cost less than $2 each today.  Spend $30 extra and get a nice, big panel.  Aim to finish with at least 50% of spaces unused. 

Don't use copper

The #2 mistake is using copper wire for feeder.  That's just silly. Not only is aluminum proven and reliable for feeder, the old feeders never had problems from being aluminum, not only did they improve the metallurgy, but the lugs are aluminum.  So the clever novice creates the dissimilar metal matchup instead of avoiding it. 

Copper is also wastefully expensive compared to aluminum, which creates an irony if the person also cheaped out on a small panel. whoo, saved $30, wasted $400. 

Honestly the main reason copper feeder exists is consumers affected by the aluminum ooga-booga. Like many moral panics, there is a nugget of truth at the center of it, but it applies to small-appliance branch circuits only (receptacles, lighting, dryers etc.), and is easily managed. No home inspector is ever going to blink an eye at a 100A aluminum feeder. 

Aluminum is a very lightweight material, almost 1/4 the weight of copper, with fewer atoms spaced farther apart.  Atoms are what carry electricity, so the wires need to be physically larger (by 2 numerical wire sizes). Even so, the wire is notably lighter. 

Wire sizes

First, at 100' of distance, you do not need a wire size "bump" for voltage drop.  The wire salesmen love to exploit two misconceptions: First, you shouldn't compute voltage drop based on breaker trip, but rather on practical load, i.e. what you actually expect to run.  (and the breaker should be at least 125% of that, for Code reasons).  Second, 3% is not in Code anywhere, and it's ridiculous. Very often, the voltage drop calcs will force you to bump wire size at 3.01% drop - the smaller size would compute to 3.35% drop, and that's perfectly fine.  4.15% is fine. 5.03% is allowable. Code is concerned with total voltage drop from the meter to the final outlet; don't allow that to exceed 8% without a good reason. 

Anyway, you're nowhere near to even needing to think about voltage drop.  Even the wire salesman won't recommend a bump before 115'. 

Given that you are at 100A, you just pull it out of NEC Table 310.15(B)(16).  Use the 75 degree C column, unless you have a cable type which mandates use of the 60 degree C column. And, you round up to the next available breaker size.  That means usually: 


100A is #3 copper ($600/100ft) or #1 aluminum ($175/100ft). 
125A is #1 copper or #1/0 aluminum (table ampacity is slightly less, but you get to round up). 


As you know, the subpanel ampacity can be greater than the feed breaker ampacity. You don't need a main breaker in the sub, if it's in the same building.

Oh. You're in PVC conduit.

Okay. Change of plan for the wires, then.  

You want to use individual wires not cable.  (the outer jacket makes cable very stiff - too stiff for achievable pulling through conduit. It can be done but you'll need an electrician's truck full of pulling tools, and the whole point of DIY is not needing to call the electrician, eh? :) 

In this case, you use individual wires.  Such as XHHW-2, THWN-2, or USE-2. (the "2" just means it's the 2nd revision of the spec for the insulation, and as such, gives it more features, such as higher temperature.) 

You aren't stuck with the cable's default ground wire size. You can use any ground wire that NEC permits (6 AWG Cu or 4 AWG Al).  Since it's an outbuilding, you will need the ground wire in addition to the ground rods.  Both are mandatory; one  takes human-generated fault current back to source, and the other takes natural lightning/static electricity to earth (which is its source). 

If you just bought the cable, then cut off a few inches and see if the wires are individually labeled with markings.  If so, you can remove the sheath and use the wires in any application their markings allow. 

If you need to run some of it openly (e.g. on joists as cable) and some in conduit, you either do the works in cable (hard pull; get bigger conduit, it'll help!) or you can transition from one wire type to the other in any appropriate (large here) junction box with permitted splices.