why are my battery cables melting constantly?

you have a dead short

Golf Mower? Is this a Golf Cart? or Lawn Mower?

Electrical tape is not a fix here.

Either you have a bad battery, starter, solenoid, or a lot of corrosion on the cables (a cable turns brittle and greenish on the exposed wires if it's internal, otherwise it's on the clamp end).

The corrosion on/in the cables reduces the efficiency of the cables, so they offer more resistance to the flow of current, and get hot!

You could also have a bad solenoid which is sticking, causing current to flow when you do not need it. They are usually only hot during startup, except for a smaller current during charging.

I would need more info to really understand your issue.

Hi ... you have a direct short from the possitve cable to the negative ground...... check from the battery to the starter.... then check all the wiring... The direct short to the negative will melt both sets of cables... . Check the ignition switch it could be there,,, Disconnect the ignition switch.. and see if the battery leads get hot... I have a feelin gthats where your problem might be....

You may even have a problem with the battery too... Try a different battery ,........ The battery may ghave an internal problem ..

Take care and becareful ... I have seen a few batteries blow up in situations like this...

You have a dead short. The insulation is melted off allowing the cable to short against the frame.