We make use of ALMA continuum observations of 15 luminous Lyman-break galaxies at z∼7−8 to probe their dust-obscured star-formation. These observations are sensitive enough to probe to obscured SFRs of 20 M⊙/yr (3σ). Six of the targeted galaxies show significant (≥3σ) dust continuum detections, more than doubling the number of known dust-detected galaxies at z>6.5. Their IR luminosities range from 2.7×1011 L⊙ to 1.1×1012 L⊙, equivalent to obscured SFRs of 20 to 105 M⊙/yr. We use our results to quantify the correlation of the infrared excess IRX on the UV-continuum slope βUV and stellar mass. Our results are most consistent with an SMC attenuation curve for intrinsic UV-slopes βUV,intr of −2.63 and most consistent with an attenuation curve in-between SMC and Calzetti for βUV,intr slopes of −2.23, assuming a dust temperature Td of 50 K. Our fiducial IRX-stellar mass results at z∼7−8 are consistent with marginal evolution from z∼0. We then show how both results depend on Td. For our six dust-detected sources, we estimate their dust masses and find that they are consistent with dust production from SNe if the dust destruction is low (<90%). Finally we determine the contribution of dust-obscured star formation to the star formation rate density for UV luminous (<−21.5 mag: ≳1.7LUV∗) z∼7−8 galaxies, finding that the total SFR density at z∼7 and z∼8 from bright galaxies is 0.18−0.10+0.08 dex and 0.20−0.09+0.05 dex higher, respectively, i.e. ∼13 of the star formation in ≳1.7LUV∗ galaxies at z∼7−8 is obscured by dust.