Here's an approach using data.table package and the vectorized colSumsfunction
Some data first:
set.seed(123)
rw <- data.frame(a = sample(12511), b = sample(12511), c = sample(12511))
Then, we will create and index using gl and run colSums per group
library(data.table)
setDT(rw)[, as.list(colSums(.SD)), by = gl(ceiling(12511/60), 60, 12511)]
#       gl      a      b      c
#   1:   1 378678 387703 388143
#   2:   2 384532 331275 341092
#   3:   3 355397 367039 369012
#   4:   4 378483 355384 367988
#   5:   5 365193 372779 388020
# ---                         
# 205: 205 385361 409004 389946
# 206: 206 407232 406940 345496
# 207: 207 363253 357317 356878
# 208: 208 387336 383786 348978
# 209: 209 186874 188616 183500
Another similar approach would be
setDT(rw)[, lapply(.SD, sum), by = gl(ceiling(12511/60), 60, 12511)]
Or using dplyrs summarise_each function, could similarly do
library(dplyr)
rw %>%
  group_by(indx = gl(ceiling(12511/60), 60, 12511)) %>%
  summarise_each(funs(sum))
# Source: local data table [209 x 4]
# 
#    indx      a      b      c
# 1     1 378678 387703 388143
# 2     2 384532 331275 341092
# 3     3 355397 367039 369012
# 4     4 378483 355384 367988
# 5     5 365193 372779 388020
# 6     6 387260 386737 347777
# 7     7 343980 412633 383429
# 8     8 355059 352393 336798
# 9     9 372722 386863 425622
# 10   10 406628 370606 362041
# ..  ...    ...    ...    ...