In SQL Server 2005, I would do this using a correlated subquery:

select dummy_id, date_registered, item_id, quantity, price,
       (select sum(quantity)
        from t t2
        where t2.item_id = t.item_id and
              t2.date_registered <= t.date_registered
       ) as cumulative
from table t;

If you actually want to add this into a table, you need to alter the table to add the column and then do an update. If the table has inserts and updates, you will need to add a trigger to keep it up-to-date. Getting it through a query is definitely easier.

In SQL Server 2012, you can do this using the syntax:

select dummy_id, date_registered, item_id, quantity, price,
       sum(quantity) over (partition by item_id order by date_registered) as cumulative
from table t;

You want something like this,

SELECT *, lag(cumsum,1,0::bigint) OVER (PARTITION BY day ORDER BY id)/60 AS grp
FROM (
  SELECT
    id,
    day,
    price,
    sum(price) OVER (PARTITION BY day ORDER BY id) AS cumsum
  FROM price
) AS t;

Working from the inside out we calculate the cumulative sum with sum() in a window function,

SELECT
  id,
  day,
  price,
  sum(price) OVER (PARTITION BY day ORDER BY id) AS cumsum
FROM price;

 id | day | price | cumsum 
----+-----+-------+--------
  1 |   1 |    40 |     40
  2 |   1 |    20 |     60
  3 |   1 |    50 |    110
  4 |   1 |    10 |    120
  5 |   1 |    20 |    140
  6 |   1 |    60 |    200
  7 |   2 |    10 |     10
  8 |   2 |    40 |     50
  9 |   2 |    10 |     60
 10 |   2 |    20 |     80
 11 |   2 |    10 |     90
(11 rows)

Notice our cumsum resets on a new day, but it persists past your 60. We need to fix that, for that we simply look at the prior row, and divide by 60. We don't want to start a new group, unless the last row exceeds a multiple of 60.

SELECT *, lag(cumsum,1,0::bigint) OVER (PARTITION BY day ORDER BY id)/60 AS grp
FROM (
  SELECT
    id,
    day,
    price,
    sum(price) OVER (PARTITION BY day ORDER BY id) AS cumsum
  FROM price
) AS t;
 id | day | price | cumsum | grp 
----+-----+-------+--------+-----
  1 |   1 |    40 |     40 |   0
  2 |   1 |    20 |     60 |   0
  3 |   1 |    50 |    110 |   1
  4 |   1 |    10 |    120 |   1
  5 |   1 |    20 |    140 |   2
  6 |   1 |    60 |    200 |   2
  7 |   2 |    10 |     10 |   0
  8 |   2 |    40 |     50 |   0
  9 |   2 |    10 |     60 |   0
 10 |   2 |    20 |     80 |   1
 11 |   2 |    10 |     90 |   1
(11 rows)

And you're done.

You need a "window" aggregate, i.e. an OVER clause in the aggregate. And because the query already has a GROUP BY, the aggregate needed is the SUM() over the COUNT(d.FK_User) you already have:

SELECT 
    u.Username, 
    -- COUNT(d.FK_User) AS UserCount,     -- if you need both counts
    SUM(COUNT(d.FK_User)) OVER (PARTITION BY u.Username
                                ORDER BY CAST(d.CreationTimestamp AS DATE)
                                ROWS BETWEEN UNBOUNDED PRECEDING
                                         AND CURRENT ROW) 
        AS CumulativeUserCount, 
    CAST(d.CreationTimestamp AS DATE) AS CreationDate
FROM data d 
    INNER JOIN users u 
    ON u.PK_User = d.FK_User
GROUP BY 
    CAST(d.CreationTimestamp AS DATE), u.Username
ORDER BY
    CreationDate ;

• The ROWS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW is not strictly needed. The default frame for window aggregates when there is an ORDER BY inside OVER () is RANGE BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW, which would produce the same results as ROWS but is likely to generate a suboptimal execution plan. See Aaron Bertrand's blog article Best approaches for running totals – updated for SQL Server 2012 for details.
• I've simplified the complicated expression that seems to just strip the time part form the datetime column.
• Removed the single quotes around the aliases. Aliases and identifiers better not be reserved keywords and not have special characters or spaces. If you do need any of these, then it's preferred to quote them with double quotes "Count" or square brackets [Count].

You can combine it like this

select month, 
       sum(sales) as month_sales,
       sum(sum(sales)) over (order by month)     as cum_sum
from   sales
group by month

db<>fiddle demo

Note : this works for SQL Server and MySQL. Tested on fiddle