I have 50 feet of #8 copper cable what is the max breaker and amps can I pull through this wire

I have 50 feet of #8 copper cable what is the max breaker and amps can I pull through this wire

You are leaving a great deal of information out. For example, what is the connection you are trying to make? Is this an 8/2 or an 8/3 cable?

Depending on the type (insulation) and connection listed temperatures the max at a 60(C) would be 40 amps. If you are using a cabled listed for 75(C) in a circuit with components also listed at 75(C) then the max is 50 amps.

The third choice would be a 90(C) would not normally be found in residential wiring because there are very few listed 90(C) devices. Most would have to be special ordered, which would drive the cost higher.

We can't really answer this unless you supply the wire type. Different wire specs have different ampacity ratings. Also the voltage of the circuit affects the answer. You need to tell us voltage, type of wire (thhn, rhw, uf... etc) for the most accurate response.

Depending on the type (insulation) and connection listed temperatures the max at a 60(C) would be 40 amps. If you are using a cabled listed for 75(C) in a circuit with components also listed at 75(C) then the max is 50 amps.I agree that this cannot be answers accurately without more detail.
The above quote is basically correct.

NM or SER cable must use the 60 deg C column in figuring amperage, so #8CU would be rated for a 40A circuit.

#8CU conductors in conduit would use the 75 deg C column since regardless of the fact that wire is rated for 90 deg C there are very few if any 90 deg C terminations and circuit breakers rated for 90 deg. MC cable also fits this description.
This would allow #8CU on a 50A circuit.