Join a lookup table with a data table

I have the following schema in my database

Neighbors: ( central_id, neighbor_id)
Data: (central_id, value)

This schema is for a convolution algorithm which for each central_id I have 6 neighbors(it is hexagonal grid)
for example here is a part of my Neighbors table

Central_id|Neighbor_id
0|1
0|2
0|3
0|4
0|5
0|6

and here is my data

central_id|value
0|20
1|1
2|6
3|1
4|6
5|1
6|0

I want to join these tables in a way that I can sum value for each central_id
my final result is sth like this

central_id|sum
0|(1+6+1+6+1+0=15)

Here is some of my tries

this query gives me the central_id|neighbor_id|value

select nb.c ,ac.c,ac.value
from 
 neighbors as nb 
inner join data as ac on nb.neighbour_id=ac.central_id

but it's result is wrong, since value is 20 which is value of central_id.
this is my second try

select c as nb,value from data where c in(
      select nb.c 
from 
 neighbors  as nb 
inner join data  as ac on  nb.neighbour_id=ac.central_id
where  and ac.c=0
)

this query result is correct. It returns neighbour_id and it's value, but I can not sum them based on central_id
If I could end up with such result my problems would be solved

central_id|neighbour_id|value(of each neighbour_id not central_id)
0|1|1
0|2|6
0|3|1
0|4|6
0|5|1
0|6|0

Can some one give me some hints about fixing this problem?thanks