I am wondering if a person can cut the ends off an extension and use it to run power from your house to a shed. The extgension cord is a heavy duty 10 gauge cord. And can you run it through conduit? There would be 20-25ft of this cord in conduit and 25ft ran in the house. I'm just looking to save some money because I already have the extension cord that I rarely use.

Why are you thinking of using 10 gauge in the first place? And how are you going to connect this wire into your home's electric? You might be going against your local wiring code using such a thick cord.

#10 is fine, for 15, 20 or 30 Amps, the increased size will help reduce any voltage drop. You can't bury it, and if it is on top of the ground, it will need Male and a female ends on cord, and be able to be unplugged, 120 volt style is OK.

Cord like this CANNOT and should not be used as a substitute for permanent wiring.

Agreed, 3/4" PVC would be nice for light electric, maybe throw in another for water, and another for Telephone, Sat, Cable, intercom, alarm wiring?
Doesn't get cheaper or easier than when the trench is open.

Stan40man has it right... extension cords are not listed for, nor permitted as a permanent wiring method.