"For a double spend to happen, someone has broadcast two transactions that share the same input and total more than the available Bitcoin.
They will both appear on the network as unconfirmed until one of them is confirmed.
Whichever is confirmed first will work, the other one will eventually be pruned from the network as if it never happened. You won't find any trace of it on most blockchain explorers (like blockchain.info)
However blockcypher.com does. This is an example
It shows the double spend warning and 0 confirmations since the Bitcoin went somewhere else.
The same transaction cant be found on blockchain.info. Example
You haven't shown any evidence of a double spend (unless I missed something, which is possible) and I haven't found any myself.
Assuming this is the players deposit address: 3JciXUmXr4oAQJxRrL51sbKNmEwM7D9g1B (It is definitely an address controlled by cubits)then there were definitely two deposits for 4 Bitcoin Each about 2.5 hours apart.
2016-10-08 02:06:23 3JciXUmXr4oAQJxRrL51sbKNmEwM7D9g1B received 4 BTC, TXID: 67643826693a43411bce4c51713b0491989d14a1346c93e7f84a21b9291e126c
2016-10-08 04:33:47 3JciXUmXr4oAQJxRrL51sbKNmEwM7D9g1B received 4 BTC95594c914e25ecca361b0885dabc663260e9b6547fdd39307810e2c93bdd2e1a
The players main address is 1GjEDytM5bKKYtcrYrrd4oDYMyryCCaQev it sent both 4btc deposits and received a bunch of smaller deposits.
These addresses were also used in transactions that shared input or outputs with the 1Gj wallet. (No other addresses were used)16ZjTc2sMwkXhiCPMs99dWfJS3sUEor2ps1LKmAMdi9g8TnzbU5FkYyy8dQZQ9WKe94r1JWii56ECnVBQp32nzrQcKdfDWQt5RkmxL
None of them are showing any double spend activity on blockcypher.
If there was a double spend attempt, what is the address that a transaction was broadcast to that never confirmed?