Correct me if I'm wrong guys, but isn't most of the ammonia and trite eating backteria in the sand and the rock? I agree that aged water is very important in the stability of the tank, but how much aged water was in the tank when you first got it? are we talking a small layer at the bottom or was it like half full of aged water? Even if it was just half full of aged water, you should be fine.
I have a 14 gallon biocube for my daughter and it's a good little tank. I got it with the protein skimmer... for another $40, it does a good job of keeping the water clean, but I would strongly recommend you put some kind of filter right next to where the water goes into the trickle area in the back... I replace that filter about twice a month, and it picks up a lot of garbage that would otherwise be settling in my sand bed. If you want to keep an anemone, you want good filtration and better flow. I had to upgrade the powerhead on my 14 gallon because it wasn't blowing enough water around. Just giving you something to consider.... it's not necessary, but the anemone will most likely want better water flow since he's a filter feeder.
Being a 14 gallon tank for my daughter, she had to have nemo with a home... so I have a small long tentacle anemone and baby percula in there, both of which are doing well. I think a big concern about keeping an anemone in a 14 gallon is that the temperature will fluctuate and could stress the anemone out... he could crawl all over your tank if he's not happy... and you want him happy. If you have any other coral in there, he could start a stinging war with them since he roams around (corals and anemones should never touch), causing futher stress, and it scars everyone (scars take a little while to heal - not long though).
But if you keep this anemone happy, and host him with a percula or ocellaris, then he shouldn't move much.
OK, so long story short - To keep an anemone in your 14 gallon:
1. TEMPERATURE! Don't let it fluctuate - If you keep the temp in your house colder, you could throw another heater in there (cheap way to help keep the water temp stable) Also, 99% of the aquarium heaters on the market are fully waterproof, so if need be, you can fully submerse them somewhere in the back chamber (for a cleaner look) or put one on each side in the back of the main part of the tank. The biocube you have came with a 50-watt heater, which should do the job if your house temp rarely drops below 65. Your tank should be kept somewhere in between 78-82 degrees, but pick a temp within that range and keep it there. It should not fluctuate, even in between 78-82,
2. Water Flow - Normally flow shouldn't be a problem, but if your biocube is anything like mine was when I first got it, then you'd have better luck with a 90-year old man blowing water through a straw than using the stock water pump. The anemone just wants a spot in wake of the powerhead somewhere and he should be happy if he gets movement, so keep that in mind when considering rock placement, and ultimately anemone placement
3. Feeding - Some of the people on here will tell you to target feed an anemone, but I don't do that with either of mine (I have multiple tanks with an anemone in each). In fact, you could kill your anemone because of over feeding. The best way to tell if you're overfeeding your anemone is if he hides behind rocks. Usually they hide behind rocks to do one of two things: Split and become two anemone's, or die. If you have a clown, he'll bring some food to the anemone (not literally bring food and throw it up on the anemone, although that would be awesome if it did actually happen, but the clown serves as a contributory part of the anemone's diet, eating bacteria and parasites off the clown). You need to throw some Zoo/phyto in the tank once a week for him to filter out. The LFS will give you the right stuff and it should be in bottle form - use brightwell aquatics stuff - best on the market and at a good price. If you did that, he'd be really happy.
4. Health - when you go to the store to buy this anemone, ask to look at the anemone's mouth. It needs to be tightly shut... if his mouth is open then he's not doing well. It's also good to ask the store clerk to show you the anemone's mouth because that means the store clerk has to touch the anemone, and when he does, the anemone should react quickly to human contact... meaning if he immediately starts to close up, then he's healthy... if he kind of just floats around like a dead fish, then that means he's a dead fish. The tentacles should be full of water and he should be fully open in the tank at the store (like mine in the pic below). When you bring him home, he may look deflated on the first day, but should be fully opened again by the second day.