Yes, with DOCSIS 3.0 and later cable modem systems, it's possible to have internet service of 500Mbps or more over traditional 75Ω coaxial copper "cable TV" cable.
As an example, let's do the DOCSIS 3.0 bandwidth math for North American markets. Each traditional NTSC over-the-air broadcast TV channel was 6MHz wide, so the cable TV providers traditionally think of all their cable bandwidth as being broken up into 6MHz channel-width chunks. The DOCSIS 3.0 spec defines modulation schemes that support up to about 40Mbps (maybe 38Mbps after overhead) per 6MHz-wide channel, and DOCSIS 3.0 allows multiple channels to be aggregated together to increase downstream bandwidth. You can buy DOCSIS 3.0 cable modems that support 4, 8, 16, 24, or even 32 downstream channels aggregated together, for up to 32 * 38 = 1.2Gbps
of downstream bandwidth. When you see a DOCSIS 3.0 cable modem advertised as "8x4", the first number is the number of simultaneous downstream channels it supports, and the second number is the number of aggregated upstream channels it supports. Note that upstream channels aren't based on NTSC channel widths and are usually much narrower than 6MHz, so different math applies.
I believe DOCSIS 3.0 for Europe and other legacy PAL markets is similar, except that those markets tend to use 8MHz-wide channels because of their PAL-based over-the-air analog broadcast channel legacy, so the math works out a little differently.
Of course, not all cable TV providers (DOCSIS ISPs) reserve 16 or more channels for use as downstream DOCSIS channels in all the markets/cities/neighborhoods they cover, so just because you own, say, a 32x8 DOCSIS 3.0 cable modem, doesn't mean you'll get those speeds. Your DOCSIS ISP has to have set up the right equipment to offer those kinds of speeds for your neighborhood, and you have to pay for that level of service.
DOCSIS 3.1, which is not widely deployed yet as far as I know, can dispense with the nonsense of treating the cable as discrete 6- or 8MHz channels, and it can use some amazingly dense modulation schemes across 200MHz-wide swaths of bandwidth to provide multi-gigabit service over coaxial copper cable. Some people in the CATV industry expect that at some point, if we don't go all Fiber-to-the-Home everywhere first, that eventually all the bandwidth of the legacy coax cable plant in each neighborhood will be dedicated to DOCSIS 3.1 or later signaling, and you'll stream all your TV and movies over IP (they call this "over the top" or OTT) so that the cable companies don't have to waste cable bandwidth by transmitting legacy digital TV channel streams (ATSC) all the time to all homes even when no one is watching.
You have "fiber to the home" your cables within your home are obviously coaxial not fiber. You are both right. – Ramhound – 2017-02-09T20:13:23.330
Since when does Ethernet cable have fiber? They are four twisted pairs of copper... – Sc00T – 2017-02-09T20:22:45.457
@Sc00T Although most Ethernet is 10/100/1000BASE-T over twisted pair copper, there are plenty of Ethernet standards that use fiber optic, such as 1000BASE-SX. – Spiff – 2017-02-09T20:27:49.053
@Spiff Thanks. I often and mistakenly immediately associate "Ethernet cable" with cat cable. – Sc00T – 2017-02-09T20:42:29.100