The Sanskrit translation of the phrase "I am a part of this universe and I have the universe inside me" can be expressed as follows:
अहं एतस्य विश्वस्य अंशः अस्मि च अहं विश्वं आत्मनि आस्ते ।
Transliteration: Aham etasya vishvasya amshah asmi cha aham vishvam atmani aaste.
Please note that Sanskrit translations can vary, and this is one possible interpretation.