<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4/A</documentType>

    <periodOfReport>2018-07-02</periodOfReport>

    <dateOfOriginalSubmission>2018-07-03</dateOfOriginalSubmission>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000716133</issuerCik>
        <issuerName>CINCINNATI BELL INC</issuerName>
        <issuerTradingSymbol>CBB</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001206921</rptOwnerCik>
            <rptOwnerName>DODS WALTER A JR</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>221 EAST FOURTH STREET</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>CINCINNATI</rptOwnerCity>
            <rptOwnerState>OH</rptOwnerState>
            <rptOwnerZipCode>45202</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-07-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>14056</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>14056</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Represents the actual number of common shares of the Issuer issuable to the Reporting Person as merger consideration pursuant to the Agreement and Plan of Merger (the &quot;Merger Agreement&quot;), dated as of July 9, 2017, among the Issuer, Twin Acquisition Corp. and Hawaiian Telcom Holdco, Inc. (&quot;Hawaiian Telcom&quot;) based on the form(s) of merger consideration such Reporting Person elected to receive with respect to all of the outstanding shares of Hawaiian Telcom common stock and Hawaiian Telcom restricted stock units held by the Reporting Person immediately prior to the effective time of the merger, as adjusted in accordance with the proration set forth in the Merger Agreement.  The proration calculation has been completed as of the date of this report and, accordingly, this report indicates the actual number of common shares of the Issuer issuable to the Reporting Person pursuant to the Merger Agreement.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Christopher J. Wilson by Power of Attorney for Walter A. Dods, Jr.</signatureName>
        <signatureDate>2018-07-10</signatureDate>
    </ownerSignature>
</ownershipDocument>
