The variational Feynman formalism for the polaron, extended to an all-coupling treatment of bipolarons, is applied for two impurity atoms in a Bose-Einstein condensate. This shows that if the polaronic coupling strength is large enough the impurities will form a bound state (the bipolaron). As a function of the mutual repulsion between the impurities two types of bipolaron are distinguished: a tightly bound bipolaron at weak repulsion and a dumbbell bipolaron at strong repulsion. Apart from the binding energy, also the evolution of the bipolaron radius and its effective mass are examined as a function of the strength of the repulsive interaction between the impurities and of the polaronic cupling strength. We then apply the strong-coupling formalism to multiple impuritiy atoms in a condensate which leads to the prediction of multi-polaron formation in the strong coupling regime. The results of the two formalisms are compared for two impurities in a condensate which results in a general qualitative agreement and a quantitative agreement at strong coupling. Typically the system of impurity atoms in a Bose-Einstein condensate is expected to exhibit the polaronic weak coupling regime. However, the polaronic coupling strength is in principle tunable with a Feshbach resonance.
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