MySQL 8.0

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WITH ids AS (
    SELECT 1 AS id FROM dual UNION ALL
    SELECT 2 FROM dual
),
months AS (
    SELECT '2018-04-01' AS month UNION ALL
    SELECT '2018-05-01' UNION ALL
    SELECT '2018-06-01' UNION ALL
    SELECT '2018-07-01' UNION ALL
    SELECT '2018-08-01'
),
yourTable AS (
    SELECT 1 AS id, 100 AS amount, '2018-04-05' AS date UNION ALL
    SELECT 1, 50,  '2018-06-18' UNION ALL
    SELECT 2, 10,  '2018-04-23' UNION ALL
    SELECT 2, 100, '2018-04-28' UNION ALL
    SELECT 2, 50,  '2018-07-07' UNION ALL
    SELECT 2, 10,  '2018-08-08'
),
cte AS (
    SELECT
        i.id,
        m.month,
        SUM(amount) AS amount
    FROM ids i
    CROSS JOIN months m
    LEFT JOIN yourTable t
        ON t.id = i.id AND t.date >= m.month AND t.date < DATE_ADD(m.month, INTERVAL 1 MONTH)
    GROUP BY
        i.id,
        m.month
)

SELECT
    id,
    (SELECT SUM(t2.amount) FROM cte t2
     WHERE t1.id = t2.id AND t2.month <= t1.month) cum_sum,
    DATE_FORMAT(month, '%Y-%m') AS date
FROM cte t1
ORDER BY
    id,
    month;

id	cum_sum	date
1	100	2018-04
1	100	2018-05
1	150	2018-06
1	150	2018-07
1	150	2018-08
2	110	2018-04
2	110	2018-05
2	110	2018-06
2	160	2018-07
2	170	2018-08