Wire and Conduit for Indoor Sub Panel with Outdoor Main Panel Through Attic
You must use the 60 degree column if your feeder is &lt; 100A.  The 75C column is allowable if the feeder >= 100A, and all the other conditions for 75C are met, which they usually are.

Using 310.15B7 (#4Cu) is out of the question.  That table is for service not feeders.  Yours does not supply the entire facility, so no go. If you want to use #4Cu you must breaker 70A, since you don't get the 100A bump.  

Keep in mind attic temperatures require a temperature compensation if they're high.  It's also good to think about voltage drop if your distance >=120 feet, but don't think too much about it - base it on actual daily load, not breaker trip, and never put 3% into a voltage drop calc.  



It's legal to run cable in conduit, it's just really masochistic.  The stuff is so stiff that you will have a bear of a time manhandling it, and realistically will probably have to call an electrician to do it.   

Also masochistic is spending on copper for anything this large. Copper is a semi-precious metal. Aluminum AA-8000 is a fantastic choice but you will need #1Al.  Aluminum requires slightly larger conduit but the savings in wire easily pays for it.   I only use copper on very short runs.  If you heard something about aluminum being bad, what is true does not apply here. 



There are several ways to do it.  


conduit all the way, and individual THWN or XHHW wires in conduit.  
conduit up the wall only, wet-location cable continuously the whole way including through the conduit.   
conduit up the wall only to a junction box, individual wires in the conduit, then a splice to dry-location cable.  The splice will be fairly expensive due to the very large junction box required and Polaris connectors, may cost more than just running conduit the whole way.   


I see no reason for liquidtight conduit.  You will still need to use outdoor rated wire or cable.  The one place it might help is keeping water out of the breaker panel if you top exit.  I strongly prefer to bottom exit for obvious reasons, but that will be quite a large radius turn.