I'm sure there's someone out there who is using this combination, but probably not very many. And if your question is "will these two work together?" the answer is "yes." But before you run out and buy an SB6183 to use with an older E3000, you should consider a few things:
First, the E3000 is almost 6 years old now, and while I know you can find refurbished ones, I don't think they are being manufactured currently (the Linksys store website says they are out of stock). Not a bad 802.11n dual band router, but when paired with the top-line SB6183 (which makes sense to use only if you have internet speeds above 150Mpbs download speeds, IMHO), you can do a lot better than the E3000.
If your cable co is offering higher tier speeds (meaning they offer 256 QAM 16x4 bonded channels), then the SB6183 is the logical (and really only) choice in cable modems that can be user owned and many cable co's are also renting them out along with other Arris combo units. But it's generally considered the fastest stand-alone cable modem available for retail purchase by end users.
If your cable company isn't offering that many bonded download channels, the SB6183 is probably overkill and it will cost you a lot more than you'll need to spend on a lower speed ISP tier, especially if you're planning to pair it with an older dual-channel router like the E3000, which has a maximum theoretical WLAN speed of 300 Mbps, and which likely won't see any speeds on the wireless side anywhere close to that.
If you already own the E3000, the only question is whether your cable company has already provisioned your area for more than 150Mbps download speed; if not, then you really shouldn't buy the SB6183, and should instead get the SB6141 (which is 8x4 and a lot cheaper), or just rent a modem from your cable provider until they upgrade your service to faster speeds.
On the other hand, if you already own the SB6183 and have the higher speeds, you should then probably get a newer 802.11ac router. Assuming you have no 802.11 ac clients yet, then I wouldn't spend the money on a 2400 or 3200 class router, and any of the 1750AC or 1900AC class routers from Asus or Netgear will serve you just fine if paired with the 6183.
Lastly, assuming you do get a new router, don't throw a perfectly good E3000 away, since you can still use it as an Access Point or Bridge to use with your newer modem, thus extending your network and/or providing additional wireless coverage in areas where your new router may not be providing optimal signal.