If you use a BLOCK_SIZE that is 32 kB or more, you will be creating strings that are 85 kB or more, which are allocated on the large objects heap. Short lived objects should live in the regular heaps, not the large objects heap, so that may be the reason for the memory problems.
Keep in mind that when converting data to base64, the resulting string will be 33% longer (assuming the input size is a multiple of 3, which is probably a good idea in your case). If BLOCK_SIZE is too large there might not be enough contiguous memory to hold the resulting base-64 string.
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