Aggregating a column only on distinct values of another column in SQL - with some constraints

Suppose we have a table like the following:

ID may repeat, while the cost associated with each ID on a given Date is always the same - that is, only Color differs. I would like to sum up the Cost for a given ID, across the Dates.

Ordinarily, you'd write a query similar to:

SELECT inner.ID, SUM(inner.Cost)
    (SELECT ID, Cost FROM Table GROUP BY ID, Cost) as inner
    GROUP BY ID;

Which would return a result like this:

However, suppose we want to also get the Color in the same query - in other words, we want a result like:

If we select Color from the inner select like:

SELECT inner.ID, SUM(inner.Cost), Color
    (SELECT ID, Cost, Color FROM Table GROUP BY ID, Cost, Color) as inner
    GROUP BY ID, Color;

The SUM(Cost) for ID = 1 then becomes 30, as it sums up the rows with both Green and Black. I haven't run the exact SQL listed, so hopefully the intent still comes through any errors that might be present. To sum it up: is there a way to select Color while having SUM ignore the extra additional Color rows?

I think the SELECT without Color could be joined with the Table on ID to pull in Color separately - unfortunately, I'm constrained in this area, working with a query generation engine and this would take significant rework. I can't really use DISTINCT on the inner query either, because the rows I want aren't duplicates. One might also suggest that the data should be laid out differently in the first place, but that's similarly outside my immediate control. Lastly, splitting it into two separate queries likely isn't an option either. Given these constraints, are there any potential solutions I've overlooked? Maybe some clever WHERE filter I can apply on the SUM?

A few approaches you could do, one is to use a correlated subquery:

select distinct id, color, 
  (select Sum(distinct cost) from t t2 where t2.id = t.id) as SumCost
from t;

with data as (
    select distinct Id, Cost, Date
    from T
), agg as (
    select Id, sum(Cost) as AggregateCost
    from data
    group by Id
)
select * from T t inner join agg a
    on a.Id = t.Id;

This doesn't assume that costs must be unique.