I feel the other two answers here are actually giving you misleading information:
If a certain cable has a bandwidth of 10 mbps, that means in can
contain 10 megabytes of data inside it at any given second.
OK first lets clarify terminology, “10Mbps” is used to denominate a unit of speed “megabits per second” which is 10,000,000 bits per second. Megabytes being 8 times larger and MB (MegaBytes) usually used to denote volume of data as a unit. I assume you meant the former, 10Mbps.
Secondly, I think you have misunderstood some basic networking aspects based on the wording in your question and I don’t think the other answers are clearing up your misunderstanding, only worsening it. There is almost no link to the length of a cable and the speed at which data is sent across it. The speed at which electrical signals travel down a copper wire is related to the dialectric constant of the physical cable and casing properties. Long story short, they can travel at nearly the speed of light, copper cabling for all intents and purposes isn’t slower than fibre optics which many people seem to think.
If you really want to say how much data a cable can "hold", irrelevant of length, the answer would be "1 bit" (a pair can be transitioning form DC+ to DC- or from DC- to DC+ at any one moment in time).
Thirdly, speed is not the same as bandwidth. In networking nomenclature we use the word "bandwidth" to describe the volume of data that was moved. We can move 10MBs (megabytes) of data and 1Mbps (megabits per second), or we can move it at 10Mbps and it will take 1/10th of the time it would have taken at 1Mbps. The speed at which data is transferred over a copper cable does not change based on the length of the cable. We can have a 5 meter cable that runs at 10Mbps, 100Mbps, 1Gbps, 10Gbps etc (there is a slight increase in delay with longer cables as I said above, the electrical signal does have to propagate down the cable, but this is so tiny it is negligible, it doesn’t change the speed of the network link).
...a nominal maximum length of 100m. Longer than that your bandwidth will most likely drop (quickly to 0). - the bandwidth doesn't drop, it either "is" or it "isn't". The data was either received without error at the speed the link operates at (10Mbps, or 100Mbps etc.) or it wasn’t and the data must be resent. This is only if you are using protocols that support re-transmission and/or you are sending data which must be re-sent (e.g. live TV streams, dropped packets are lost and not usually retransmitted). Since speed and bandwidth are not the same thing, it is possible for the error rate to increase without the bandwidth dropping by sending larger frames or packets for example, so few packets need to be successfully send and received because they carry more data.
so no it does [not] increase with length (again, rather decrese) - nope, bandwidth is not dependent on length. Again, the misuse of phrasing is making things unclear. I take bandwidth to mean "the goodput of data successfully transferred".
The original Ethernet specification limits the individual copper cable lengths to 100 meters, because of the latency time of getting a packet from end-to-end then getting the returning ACK before timing out. - No. ACK is something that happens at the transport layer in TCP. The length of 100 meters likely stems from CMSA/CD (Carrier-Sense Multiple Access with Collision Detection). This is the process of listening on the wire for a specific time, to check if another device is transmitting, if no device is transmitting (nothing is received) then it is assumed to be safe to transmit without a collision occurring. How long should we wait before we know its safe to transmit? We wait as long as it would take for the signal to travel from a device 100 meters away!
For instance: when you are transferring 10 MB of data, longer cables will be a bit slower to transfer that total amount than shorter ones simply because the signals travel at about 2/3 of the speed of light in copper. More length means more latency. - this is a bit of misnomer. I touched on it above. The increase in delay from the extra cable length is so small it has no measurable impact. Wikipedia (https://en.wikipedia.org/wiki/Speed_of_electricity) lists the speed of electricity to be in the range of 50%-99% the speed of light. At 0.5 c it takes 0.0000006 seconds for the electrical signal to travel 100 meters. For a 10 meter cable it takes “one less zero”, 0.000006 seconds. This has no measurable impact on you day-to-day application performance. What does have an impact is the operating speed, such as 10Mbps or 100Mbps. On a 10 meter length of Cat5e cable running at 10Mbps you will only get 10Mbps, no more, no less. Equally, if you now connect that same 10 meter length of Cat5e up at 100Mbps it will run at 100Mbps, no more, no less. What really makes a difference are factors like the encoding scheme used (https://en.wikipedia.org/wiki/64b/66b_encoding), serialisation delay, the error detection and correction methods used (see https://en.wikipedia.org/wiki/Reed%E2%80%93Solomon_error_correction and https://en.wikipedia.org/wiki/Hamming_code), etc. This is because as the length increases so will the attenuation, NeXT, FeXT (https://en.wikipedia.org/wiki/Crosstalk and https://en.wikipedia.org/wiki/Attenuation-to-crosstalk_ratio) etc. resulting in (eventually) data loss.