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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

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

    <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>35142</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>35142</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Represents the maximum 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 assumption that the Reporting Person elected to receive common shares of the Issuer as the sole form of merger consideration 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. Such election is subject to proration as set forth in the Merger Agreement and the proration calculation has not been completed as of the date of this report. Thus, it is not possible to determine the exact number of common shares of the Issuer issuable to the Reporting Person pursuant to the Merger Agreement.</footnote>
        <footnote id="F2">(Continued from Footnote 1) Once the proration calculation is completed in accordance with the Merger Agreement, the Reporting Person will file an amendment to this report disclosing the exact number of common shares of the Issuer received by such Reporting Person as merger consideration. The closing price of the Issuer's common shares on July 2, 2018 was $15.65.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Christopher J. Wilson by Power of Attorney for Walter A. Dods, Jr.</signatureName>
        <signatureDate>2018-07-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
