The outposts come in sets of 3 up until the last one totaling at 11 outposts. Each following set uses a rarer core to power it. However if you abandon an outpost you do not lose those power cores.

Now for the first 3 outposts after your command center you will need 5, 10 and 15 base power cores which are the easiest to find. For the next three bases which will number 5-7 you will need base fusion cores and take 5,15 and 25.  The next three bases will use base plasma cores and my guess is it will take more cores then the previous set making it very hard to get the full 11 bases together without paying real money.

Price Core:

1/ Power Core: 100 golds/each

2/ Fusion Core: 450 golds/each

3/ Plasma Core: 750 golds/each

4/ Ion Core: Need 30 buildings level 15 at the same time.

Base Core Requirements
1 Home Base No Core Req
2nd Base 1 Power Core
3rd Base 5 Power Cores
4th base 15 Power cores
5th Base 5 Fusion Cores
6th Base 15 Fusion Cores
7th Base 25 Fusion Cores
8th Base 10 Plasma Cores
9th Base 25 Plasma Cores
10th Base 45 Plasma Cores
11th Base 1 Ion Core (Earned only by a mission that appears after you achieve your 10th base. In order to complete the mission you must have 30 level 15 buildings at once.