Simple wire continuity tester, but also needs to check shorts
Figure 1. A 555 pulse generator driving a CD4017 ring counter will do the job. Image source: Electronics Hub.
You just connect your wires between the 4017 pins and the LEDs. On a good cable each LED will turn on in sequence, one at a time. A missing LED will indicate a break and a double will indicate a short. The 4017 can be daisy chained to expand for any number of cores.
See the linked article or thousands of others on the web. Once you get the idea then read the datasheet to help your understanding further and to learn how to read datasheets. Have fun.